Your examples are from the friggin' 60s, where sophisticated computers were pretty much nothing more than a wet dream.
The EMH is a different beast. The idea behind it is sound, but the writers constantly confuse the hologram (which is just the visual representation, NOTHING more) and the actual program behind it.
That they can't create backups for the entire modified/evolved EMH is silly, but not that silly. If an AI grows really complex, it might be impossible to back it up as a whole, and recreate an identical version from those backups.
The EMH DID have an episode where his program went nuts because of a contradiction. But that was a complex moral problem that might be believable for a complex AI. It wasn't just a simple boolean logic problem.