I think that if this is the case, you are presenting it wrong. Business types are very familiar with the tradeoffs of debt financing, you have present it as being paid in effort vs. $ (which after all, have a close relationship) and they will immediately understand that a large technical debt means you can get less desired stuff done for the same input of effort. And then you collectively decide.
Agree you have to be careful about what you present as technical debt. If you need buy in from the business side, you don't want them thinking "that's just what they say when they want more time, it doesn't mean anything". It has to be pretty concrete.
If that were literally true, then every new development would rationally necessitate a total rewrite of the codebase.
You might have meant that parts of the existing codebase would need to be changed to adapt to the new development, but as long as you've made a rational decision to keep using parts of the existing codebase, it must have been a net positive otherwise you'd just throw it all away.
So yes, the core idea of technical debt resonates with developers, but not with business stakeholders. So if you really think the business is going to be okay with "we're gonna slow down our time-to-market and say no to all your requests for a while because we need to pay back our technical debt" (which is something I see happening over and over again), you're just keeping them out of the loop and taking over their responsibilities without actually having their accountability. Developers shouldn't decide whether time and money should be invested in time-to-market and quality or feature delivery, but that's effectively what's happening when business is not involved in the tech debt discussion. This only leads to friction and suboptimal results.
That's why I think we really need to be careful when using the words "technical debt" and not just label everything we don't really understand or think can be improved as "technical debt". Challenge yourself: what really is the problem with this piece of code, other than that we don't like it?