I feel like there's an alternate wording for this advice that is less "cut corners" and more "determine how many corners you don't want cut".
Maybe involving a target condition? You want to make the best thing possible. Keep on aiming for the best, but establish a baseline that you would find acceptable. Maybe you won't make something perfect, but you'll now have a target that you _can_ get to.
This thought process reframes the discussion of "good enough" away from "did I spend enough time on this? Surely I can spend another week and make it 10% better" to "Does this meet the requirements". There is no longer a debate to be had, just a yes or no question to answer.
So when people ship things that just aren't good enough you don't have a discussion around spending more time on things or being more careful, you have a discussion around what your baseline requirements are (which is _actually_ what you care about).
Perfectionists undergo a similar phenomenon, I'm told. After all, the modern "Do it badly" movement was itself a response to the corrosive effect of the "'Good enough' isn't" message permeating all of society. I'm not unsympathetic. In solving one problem, it didn't exactly create another -we've always had perfectionists to some extent- but it made that problem much, much worse than it had once been. But the fact is, it was done to solve a real problem in its own right, and that problem has not gone away.
What it comes down to is conflicting needs. The all-pervasive "'Good enough' isn't" came about because some people genuinely need it, and they genuinely need it at that level. The same is true of the now-pervasive "Do it badly": it is genuinely needed, and at this level. And you can't balance them, because they inherently undermine each other. So what do you do?