I wish it were that simple. But I think the problem is tougher than that.
I think that the most productive way forward is to start from the premise that the business does understand technical debt, but that they don't have enough visibility into how much has been accumulated, and what the likely effects of that debt load are. They need to be kept updated about how the technical debt is slowing development, causing more issues to be found in QA, requiring developers to work extra hours, increasing the frequency of production issues, etc. I'm a believer that open, clear communication really does improve decision-making and relationships within the business.
Unfortunately, I think it's often true that the business does understand technical debt, and it's consequences, and that they've consciously decided that those consequences are acceptable, even if they make the dev team miserable. If that's the case, your best option is to keep an eye out for a happier place to work, and move if/when you can.
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