I think you underplay the importance of tech debt over time. It doesn't take long before features cost 2x or more to deliver due to tech debt, and as long as you leave the crappy code in, your other code has a bunch of workarounds in it that will also have to be rewritten when you refactor the original code. So the longer you go without paying down tech debt, the harder it becomes to get management approval to do it (because the length of time you need to stop and just fix your code gets much higher).

It's our jobs as developers to protect management from themselves and just write the code the right way in the first place, even if there's a slight hit up front.