There is a subtle reason why it might not be good: Sometimes, the blame for breaking something really should be placed on the individual who wrote fragile code without automated tests, not the one who broke their code by making a should-be-unrelated change somewhere else.
One imaginable example is when someone programs against an interface in a way that assumes behavior specific to the implementation du jour, but not guaranteed by existing contracts. Then someone else makes a change to the implementation that fits in the contract, but breaks the depended-on code. No tests fail because no tests are written for the depended-on code. Who's really to blame?
The purpose of this isn't to blame people, but to understand responsibilities, and if "You break it, you buy it" is really such a good policy.
EDIT: I really worded this poorly. I meant it to be about how to write correct software with respect to dependencies, including hidden dependencies. I meant this to be a question of what a programmer's responsibility is to avoid bugs, not what to do when a surprise bug is found. BUT, since so many answers have been given already, I'll let the question stand as-is and indicate an answer accordingly.