I heard a great quote yesterday:
You can't out-exercise a bad diet
And this is a great metaphor for technical debt.
We all agree that you need to pay down your tech debt in your software. And it's great to commit to addressing a little technical debt during each sprint. The problem is that this is the exercise. And if you still have a bad diet of cutting corners and taking shortcuts, your stuck with an overweight system (a monolith, if you like).
If you want to get serious about the technical debt, you need to start by fixing your bad diet of shortcuts and start by doing things right while doing the right thing. Only then can you really start paying down existing technical debt as well.