You have it completely reversed, a rock solid codebase is much more important in an agile environment than a waterfall one. In waterfall you just need to tick the feature boxes. In Agile you not only need code that readily accepts changes, but you need to provide visibility to the business side about the state of your technology so they know not only the opportunities but also the costs of the problem.

The only reason why this becomes a phase that burns developers out is that writing high quality software is hard, under-appreciated and needs to be painstakingly learned by experience and guidance by experienced mentors. But most projects in the industry are complete shitheaps where the seniors need to spend all their time fighting fires instead of teaching the craft to juniors. No wonder developers get burned out.