This actually seems like a really important idea absolutely deserving of its own blog post.
I'd have to think about the exact argument for why this feels so right, but the kernel would go something like this: whatever you build on those parts of the codebase where you have technical debt incurs new technical debt, because you're building on top of abstractions you'll remove later. The reason you have to remove the new abstractions, too, is that abstractions are like puzzle pieces: their structure determines which other abstractions they can connect with. So, as a rule (there are some exceptions), you can't take out one bad part, replace it with another, and leave everything around it untouched.
And, of course, it's easier to build on top of something creaky but currently serviceable than it would be to first rip that out and replace it, so that's what you do in most cases ... and the whole codebase gets more creaky and less serviceable; you increase the amount of abstractions you'd have to rip out and replace before building something new. The problem does, indeed, grow exponentially.
The argument is free to a good home -- I don't have the time for a full, meticulous elaboration, but I'd love to read one if someone is interested in making it.