I agree that there's no overarching rule that makes the tradeoffs easy to analyze.

I will, however, say that after working on the same code base for over 7 years now, and watching the company grow from 15 employees to 400, I can't imagine ever working at a place that didn't have a large investment in unit tests, tech debt elimination, automation, etc. Without that stuff, our products almost certainly would have collapsed under their own weight by now, and our ability to ship predictably and on-time would be gone. Even within the company, we have some groups that have done better than others as far as automating tests (both because of team personality and because of technical issues that make certain types of features harder to test), and it's quite obvious that the groups with the best testing are the groups that are able to make much more predictable progress and that are able to ship on time. The groups with less-good testing tend to be prone to fairly massive schedule slippages due to a ton of late-stage regressions that only get caught when they ship their code out to their internal users.

Once things get to the point where no one person can reasonably understand the full implications of their changes, because the system is just too big and complicated, if you don't have unit tests you're in big, big trouble, and you need to reduce tech debt so you can keep things as comprehensible as possible. Even then, of course, you have to constantly decide how much to invest in testing and infrastructure and cleanup versus how much you invest in forward progress, and there's never an obvious equation that will give you a right answer.

If your code base and team are small and likely to stay that way, such that you can still mercilessly refactor and change the code without introducing a bunch of hidden bugs, then testing doesn't matter as much. If you ever expect the code to get to the point where that becomes less true, and where the possibility of introducing errors increases, then it starts to matter a whole lot more.

Hypothetically, let's assume we built the same product with two teams, one that did a bunch of unit testing and one that didn't (call them Team A and Team B). From my experience, what essentially happens is that Team A ships version 1 first, ships version 2 first but takes about as long to build version 2 as Team B, ships version 3 about the same time (since it takes them longer to build it), experiences a massive schedule slip in version 4 (since the complexity catches up to them and things becomes buggy and they start playing whack-a-mole with bugs), and don't really ever ship a version 5 because their code has so much tech debt that no one can change anything safely without breaking something else unintentionally, and they start contemplating a complete rewrite of the code base. Again, totally contrived situation (it doesn't have to go that way, Team B could still totally screw things up anyway, etc.), but that's roughly what I've seen happen, both at my company and at others.

I don't think it's fair to say that consultants push TDD and tech debt reduction because that means the project will take longer: that's a bit overly cynical. Many, many organizations use unit testing and such in house because it has a huge long-term benefit (as well as generally more predictability in the short term, which is often more valuable than absolute speed), not because some consultant told them to do it.