Getting pre-approval consensus is not really the way to go about those things, at least not in that kind of environment. Anything "important but not urgent" will not get the sufficient level of consensus. Generally if you're faced with a problem where you're certain people will find it worth the effort after it's done, but where you can't get approval beforehand, going skunk is the only way.
Most of my steps forward in technical reputation have been from those efforts.
This might surprise you but people don't like you fixing their mess behind their back. They take it as personal insult. They correctly recognize that you think what they did is messy and bad and you fixing it looks to them like an attempt to dethrone them from whatever little position they have carved for themselves within the organization.
This comment echoes that sentiment a bit, I think; there's an implicit dependency in there on the project not having a collective structural investment, whether that's explicit (overt, with explicitly delineated boundaries) or implicit (implied, fuzzy, part of collective culture), on the thing being fixed.
And then maybe the biggest problem is the whole "putting in extra voluntary work" thing. Higher risk of burnout because you're spinning too many side project plates. Either your main work gets impacted, you start putting in overtime, or management starts thinking they're not giving you enough work, if you have all this time to do side stuff.
I've tried the advocation thing several times, but it usually ends up being you volunteering to do a lot of extra work. And then working extremely hard to try to gather some sort of consensus or buy in from the team, and receiving either push back or non response at every step.
I've now decided to just try not to care as much. I focus on writing my tasks to the best of my ability and improving whatever small bits of code that I can along the way, but I now just consider the codebase the property of the CTO and engineering management. If they want me to focus on helping fix what's broken, then they need to assign me to it and allocate time for it.
That kind of sucks too and takes some of the joy out of work, but at least I'm less likely to overwork myself again.