I've been mulling over how the bitcoin protocol is basically defined by the code in Bitcoin Core, a few scattered BIPs, and some dev docs. It's done alright for like 17 years but there are times when different interpretations slip in between implementations and even updates to Core. We’ve seen some weird situations with block acceptance and mempool rules that could potentially cause chain splits if nobody catches them.
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Maybe, but it’s complicated. Bugs can pop up everywhere, like in assembly, compiler, and OS levels. Even if you prove the code is correct, it could still run wrong for various reasons. A perfect program can still get interrupted, and restarting might trigger bugs. Bitcoin Core relies on users not messing things up, and if they do...well, that's when things get unsafe.
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Totally agree on the distinction. A formal spec isn’t about wiping out every single bug out there. Like you mentioned, hardware and OS issues can always mess things up. But if two separate implementations are based on a verified spec, it could really cut down on the discrepancies in interpreting protocol rules. Not bug-free, but definitely less room for confusion.