>

I assume you're referring mainly to national elections. Consider local ones. Local politicians are certainly not immune to bribery but there is a LOT on the ballot at the local level that shouldn't be overlooked.
I live in California. The ballot proposition system here alone is evidence of the kind of power — too much power, IMO — that voters have. Essentially, anyone can get any item on the statewide ballot if they collect enough signatures. In the 1970s we passed Proposition 13, which capped the amount that property taxes could increase every year that you owned a home. It completely reshaped our housing system, determined who stayed in their homes and for how long, determined who is now able to buy a house where, determined school funding. Money swayed this fight in a big way (as it does with many of the propositions year after year) but votes allowed it to happen. So even if this doesn't counter your argument about voting not being enough to push toward real problem solving (especially since I think the ballot proposition system has basically been commandeered by special interests with deep pockets), i think it does show that voting (or not voting) makes a huge impact. 
There's a ton of other seats we vote on at the local level that make huge differences on a daily basis. We vote for school board members. Judges. District attorneys. The candidates who run for these seats can be radically different from each other, and voter turnout for local elections is often painfully low even though these offices affect our everyday lives much more directly than those at the national level. 
And if you're still disheartened by the fact that money has a big influence over votes, I think there are a lot of local examples that have shown that money alone isn't everything. Los Angeles had a billionaire run for mayor who spent literally $100+ million on his campaign and lost. We also saw established, well connected political candidates lose to first timers who spent half as much on their campaigns. It happens, and it does make a difference.
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I’ve spent some time working in political campaigns, and I think most voters would be surprised to learn just how slapdash most political organizations are. A lot of the time, when people hold views like the one you’re sharing here, I get the impression they imagine political machines as powerful, robust, and precise—but the reality is a lot more chaotic. There are people running around like headless chickens trying to figure out what the hell the voters want, and it’s getting harder and harder to tell these days because polling is so much less reliable than it used to be. 
But anyway, when it comes to your view, I think you’re right up to a point. Money has too much influence, and far too large a percentage of our political class is concerned with money above all else. That’s bad. 
But, the truth is that the voters always get final say, and I’ve personally witnessed several races where the side with the most money didn’t win. Increasingly, I see the problem of cynicism as being worse than corruption, as cynicism can create self-fulfilling prophecies. Politicians know what gets them elected—that’s what they’re good at—and if their voters are deeply cynical and apathetic and hard to reach, that ironically makes big donors and lobbyists more powerful. 
Anyway, the overall point is that we as voters have a lot of power over what elected officials do; the fact that we fail to wield it well explains a lot of what’s going on now. >

The cynicism comes from feeling that rich and powerful people are controlling the system, not the people. >

Dude is just lobbying to keep his job >

By “working” maybe I should have said “volunteering.” I’ve never been paid to work on a campaign, but I’ve logged lots of hours block walking, passing out flyers, trying to register voters, etc. >

I admire you. >

It's really not hard! If you've got an extra hour a week to spend on something, you could start showing up for local political stuff. You quickly figure out who the good and people are in that space. >

If you think money grants so much control over elections, why is so little of it spent on elections?  
The total amount spent on all House and Senate elections in 2022 was 9 billion, or less than 5% of the money that Elon Musk lost this year. Or 1 weeks worth of revenue for Amazon or Saudi Aramco.  Why spend 44 billion on twitter if you could buy every seat in congress for 20% of that price?
The average house of representatives member spends 2 million dollars on their election, this  is chump change.  If you could buy control of congress for so little money, why didn't a rich democrat donor do it this midterm? If congress seats are up for sale shouldn't there at least be a bidding war to drive up that price?
Why did Michael Bloomberg, by far the richest person in the 2020 Democratic primary get destroyed?  Shouldn't he have just been able to sway the primary with his money?
If corporations could easily spend money to change policy, why do regulations like Dodd-Frank get passed?  It costs banks more than 50 billion dollars per year, shouldn't they have just spent a few billion to buy off congress to not pass it, or spend a few billion now to get it repealed? Why do the EPA, SEC, or FDA exist, and cost hundreds of billions of dollars for corporations every year?  Shouldn't it be easy for corporations to just buy the influence they need to get rid of those costs?
Charities like United Way or Habitat for Humanity raise billions of dollars every year, why don't they just pay off the government to get the changes they want enacted?
The truth is that money just doesn't have that big of an impact, and that belief doesn't align at all with reality when you examine the actual amounts that get spent. >

I read a George Will column long ago where he noted that spending on a presidential election (both sides) was substantially less than Americans spend on Halloween candy in a given year. Now, in recent elections, I think that has flipped, but presidential election spending is still on the same order of magnitude as Americans spend on Halloween candy.