But - sometimes drastic measures and hurt feeling are needed to break out of a bad attractor. Just be sure you’re OK with leaving the company/org if your play does not succeed.
And know that as the OP describes, it’s a lot about politics. If you convince management that there is a problem, you have severely undermined your technical leadership. Game out how that could unfold! In a small company maybe you can be the new TL, but probably don’t try to unseat the founder/CTO. In a big company you are unlikely to overturn many layers above you of technical leadership.
This is why I incessantly preach to my coworkers: "you are not your job". Do not attach to it emotionally, it's not your child, it's a contraption to solve a puzzle. It should be easy and relieving to scrap it in favor of a better contraption, or of not having to solve the problem at all.
Just like every league of legends game, it's not possibly your fault!
This is actually harder for more senior/managerial folks, as often they'll build/buy/create something that's big for their level and now they're committed to this particular approach, which can end up being a real problem, particularly in smaller orgs.
Once upon a time, I worked for a lead who got really frustrated with our codebase and decided to re-write it (over the weekends). This person shipped a POC pretty quickly, and got management buy-in but then it turned out that it would take a lot more work to make it work with everything else.
We persevered, and moved over the code (while still hitting the product requirements) over a two year period. As we were finishing the last part, it became apparent that the problem that we now needed to solve was a different one, and all that work turned out to be pointless.
It's how they get to be the experts that are needed.
Replacing their code IS replacing their expertise and therefore them. How would you expect words to change that?