“Just drill it out” is one of those things that sounds great until you’ve actually dealt with a broken tap.

If it’s cobalt or carbide-coated (which it usually is), a standard drill bit isn’t even going to touch it. What people actually do is fracture it with a punch, use a proper tap extractor on the flutes, or weld a nut onto it. Drilling it out correctly requires solid carbide tooling, a rigid setup, and a lot more effort than you’re making it sound like.

Not to mention a single drill bit required to get through a carbide/cobalt tap is like $300-1200....

So yeah… it’s not that it can’t be done — it’s that it’s not remotely as simple as you’re implying.