If by "exploratory testing" you mean things like clicking around on a site manually, then sure it can be useful to spend a couple of minutes looking for anything dodgy.

That doesn't mean engineers are paid to go through a list of regressions and edge-cases, look for broken links, double-check calculations with pen-and-paper, etc. All of that can be done across an entire site automatically in seconds; there's no excuse not to.

> a) users do crazy things

Again, thinking we can check such things better than a computer is misguided. Test frameworks like QuickCheck can stress-test a system with far more strange inputs/transitions than I could hope to think of.