Replace Messages app with something else and have it use my phone number? Is there a way for me to use a different app to send/receive SMS messages on my iPhone, and still use my same phone number?
It'd be great if it could become the default for sending messages on my iPhone, without jailbreaking.
So I'd like an app that

defaults to sending SMS messages, even for contacts that have iMessage
reuses my existing phone number when sending/receiving SMS messages

So in theory, it's like I have an Android phone, and only know how to send/recive SMS messages ;-)
EDIT: Note my main problem is that when I have iMessage disabled, other people still try to send me iMessages, which I dont get if I have iMessage disabled of course!
According to a third party wanting the same, Apple doesn't allow this: https://support.signal.org/hc/en-us/articles/360007321171-Can-I-send-SMS-MMS-with-Signal-

There was once an app which synced your sms and allowed sending and receiving through an app: mysms. It would still work if you put the sim card into an android phone, but that doesn't seem to be what you want, as you'd now need another phone number for calls on your iphone...

The closest you can get on an iphone is probably through your provider's sms website offerings, like this one: https://n.vodafone.ie/business/products-and-solutions/mobile-communications/bulk-texts.html

Depending on your provider, you could probably put a shortcut somewhere on the iphone which opens a page where you can see your sms inbox and write new ones - with some business features on top.

Then you just need to deregister your phone number from imessage and make it work with your email address only. Anyone entering your phone number on imessage should then get to send the message in green.