The biggest issue I've seen with not handling tech debt on an ongoing basis is that there's never a good time to start. So if it's not built into the development cadence, then resistance builds for doing it at all. Product starts pointing fingers at the "slow" engineering, who point back at the "breakneck" demand for feature work, and negotiations start for unrealistic (for both sides) halts in development - neither sufficient to resolve the problems nor short enough to avoid hurting the business. Then product breathes a sigh of relief - the tech debt is "resolved" and will never need to be addressed again, engineering returns to wading through the codebase that is only marginally less swampy than it was before the cursory refactoring sprint, and the downward spiral (and finger pointing) resumes.

At least that's how it always seems to happen around me :)