The problem with that mindset is that testing, like verification, becomes extremely powerful as it becomes more automated and you throw more compute at it. And it's arguably easier to automate testing than it is to automate formal verification.

Sure, testing isn't perfect. But is finding 100% of the bugs that much better than finding (say) 99% of them? This is especially the case if the missed bugs tend to be those that happen very rarely.

A formal specification allows automatic generation of tests. So run billions of tests, randomly generated, and see if any violate the specification.

Even theorem proving systems use this sort of thing as a short cut, for example pruning off attempts to prove a universally quantified statement by looking for counterexamples.