>

I don’t think it would be a magical solution, but if we’re being honest, it could be a better one. Batman has been doing his thing for a long time, and hasn’t made any significant improvement in the lives of your average Gotham residents. Things are still just as bad as they were before he started. 
Might as well try something different.
So Batman/ Bruce Wayne grew up Rich. Had a shitty childhood, parents where killed in front of him for “ money”. And Gotham is surrounded by multi-millionaires ( referring to court of owls). 
Superman ie Clark kent grows up in smallville on a farm in a little podunk town. And Clark Has a healthy childhood ( minus the superpowers). But Martha and John grow to be old on the farm. Clark doesn’t “become” Superman till after he moves to metropolis. 
The point I’m trying to make here is that gothams problems are not something more money could fix. It’s a societal thing that needs to be fixed. 
Simply put- Money don’t buy happiness. >


It’s a societal thing that needs to be fixed.

Yeap.  Gotham and the real world are the same in that regard.
All of us can see the biggest things wrong with society (money in politics, for example) but no one does anything about it.  That's because the people at the top don't want it fixed. >


All of us can see the biggest things wrong with society (money in politics, for example) but no one does anything about it.  

Iiiiii… don’t know if that’s true, the whole ( all of us can see the things). There’s a good majority of people in the real world who agree with the elites. 
But the same goes for Gotham. Think about it someone voted Oswald in to be Mayor. 

That's because the people at the top don't want it fixed.

See here I’ll agree that they don’t want it fixed. But at some point the people do need to take some responsibility. They are voting them in, they are allowing these people to run amok in their city. 
And that’s why Batman ( not Bruce) the actual Batman does more for Gotham than Wayne money. Batman is a symbol of standing up to the corruption and the criminals. Which will inspire the citizens to stand up as well. >


You're still gonna need a smart, well-trained ninja

In the grand scheme of things, do you really need a ninja? Like, actually? Is there any scenario where pouring of billions of dollars of tech into one guy who runs around and punches people actually makes sense? >

Exactly, batman has been as this for years and has he made any meaningful progress for Gotham City? 
(Depends on what universe you look at) >


Exactly, batman has been as this for years and has he made any meaningful progress for Gotham City?  
(Depends on what universe you look at)

Gotham was already headed for hell on a train with no brakes and no conductor.  I like to look at it as Batman finding ways to slow the train and get people off safely where he can.
Has he lowered the crime rate?  No.  Did he prevent a mass casualty event and stop the city's complete destruction on numerous occasions?  Yes.  I wonder where that rates on the "meaningful" scale. >

Practically every "super villan" in Gotham were created by Batman. It wasn't super serum powered undead giant that killed his parents, it was thugs. But after bat hit the scene Arkham was filled with super powered lunatics.
Without bat we wouldn't have to worry about city scale attacks from laughing plant ninjas. >


Without bat we wouldn't have to worry about city scale attacks from laughing plant ninjas.

Poison Ivy was a rich girl who was experimented on, went insane, and became an eco-terrorist.  If Bruce had died with his parents and never became Batman, nothing would change for her (except maybe her plans to destroy Gotham would more likely succeed).
Penguin, a bullied outcast from his family turns to crime.  Again, Bruce not existing changes nothing for him.
Firefly, a pyromaniac criminal, his origin having nothing to do with Batman.  Mad Hatter started off killing people in high school, again nothing to do with Batman.  Victor Zsasz was a hitman for the mob before Batman.
The often-repeated sentiment that Batman created his villains is horsepoop that can be disproven with a little research. >

In fact, one Batman the Animated Seried episodd features all villains making a mock court against Batman, trying to prove that he is responsible for their crimes, only to realize that sithout Batman they'd wind up the sake. >


Can you convince me that Gotham City, as written, would be better if Wayne quit being Batman and put most of his money into the city?

No, but maybe I can convince you that he already does that (the money part). Bruce is already one of the biggest philanthropists in the DC world. Medical centers, job training, soup kitchens, infrastructure programs, scholarships, orphanages, anything that exists to help the people of Gotham exists because of the Wayne Foundation. 
People who say he should pay more taxes, and that that would help Gotham don’t understand how taxes work. The city would never be able to tax Wayne in any substantial way. Any increase in taxes he’d face for amounts that would materially affect Gotham’s budget would come from the state, or the federal government, and they wouldn’t give it to all to the city. And even if Bruce lobbied for increased taxes on billionaires, Luther would oppose him and outspend him on lobbying. He doesn’t spend his billions on charity like Bruce, so he’d just buy or threaten congress until they killed the bill. >

Which is pretty realistic when you think about it >

I’m convinced Lex knows Bruce is Batman, and just sits smugly with the knowledge that Wayne Industries will never be able to overtake Lexcorp because Wayne spends all of his time punching mental patients at night while Lex is making shady land deals and stealing cakes. >

The complex problems of Gotham would not be solved by simply throwing money at it, so it's not a magical solution. Minor spoiler: in the most recent movie it's stated that (20 years ago) Thomas Wayne spent 1 Billion Dollars trying to fix these problems and it didn't work.
The more sincere statement of this opinion is that Bruce Wayne spending nearly all his time, money and effort on Philanthropic endeavours; would be better than him being Batman. 
Issues like obesity, homelessness, health care and drug addiction lead to 1000s of death every year. The correct allocation of resources can reduce these deaths significantly. It wouldn't happen overnight.
It's difficult to know if Batman makes crime problems better or worse. It could be argued that criminals are getting more violent to counter Batman, a tactic that would get them shot and killed if they did it to the police. >


Minor spoiler: in the most recent movie it's stated that (20 years ago) Thomas Wayne spent 1 Billion Dollars trying to fix these problems and it didn't work.

This is for reasons I've mentioned on other comments; the people controlling the money are corrupt.  They've been using the Thomas Wayne fund to get money into the pockets of the wealthy elite.  That's why your statement here..

The more sincere statement of this opinion is that Bruce Wayne spending nearly all his time, money and effort on Philanthropic endeavours; would be better than him being Batman.

It just doesn't ring true for me.  There's been deep corruption in Gotham since its founding.  Even if Bruce retired as Batman forever and blew up the batcave and did exactly what you said, it wouldn't help Gotham because the stuff going on there is by design.
The revolving door at Arkham and Blackgate.  The reallocations of as much money meant to help the poor and working class to the wealthy as possible.  The criminal organizations that existed before Thomas Wayne died (like the Falcone crime family and so on).  The Court of Owls pulling the strings.
Before any of the philanthropic endeavors can succeed, those elements have to be taken care of.  They otherwise will control or loot the money meant to improve things for ordinary people.
If the criminals weren't leveling up fighting Batman, they'd be leveling up fighting each other over territory.  I would argue that Batman definitely makes it better because he's literally saved the city and prevented mass casualty events on multiple occasions. >

Philanthropy and organised crime are not necessarily mutually exclusive. Sure more money will get lost to corruption, but it is possible to do some good. The deaths due to things like obesity and drug addiction are not as obvious as people who are killed by the Joker. Saving people from drug addiction doesn't feel the same as saving them from a villain in fancy dress, but it still counts. 
The levelling up that Batman causes is different to from criminals fighting each other for one very specific reason; Batman doesn't kill. If you attack another criminal gang more aggressively, you are more likely to die. The same is not true with fighting Batman. >

Gotham is supposed to be hell on earth. An allegory for crime which is why Batman is “needed”. I think a lot of people tend to miss this