I think that rewrites are an important part of how software is written, and it's an important part of being "agile", in the sense that you can go in and write a prototype that's coded very simply without much regard for long-term architecture, knowing that requirements likely will change and that you likely won't get the design right on the first go anyways.

Coding is like writing, in the sense that it's often faster to write a sloppy first draft followed by a better second draft than it is to agonize over getting the first draft right on the first go. The first draft is generative. Its purpose is not to be good but instead to let you get something built quickly and to let you explore the problem, so that you know what edge cases you'll need to account for in your final architecture.

But this still of working will never get through management because the moment you show them a working product, they'll tell you to ship it and won't give you a chance to rewrite.

I think the best way to solve this is to flatten the hierarchy. Get rid of the notion of managers who rule over engineers and give ownership of the code back to the engineers. Have the engineers and product "owners" make decisions together in a democratic fashion.