And we'd also need to *fix* all pages with this syntax, and we can't really fix automatically, need to check on a case-by-case basis.
Why not? The current parser manages just fine with it, you could write a bot that changes everything with the same rule.
The proposed change is just that ''' always opens a bold tag and '' always opens an italic tag, not having to check *the entire wikitext* for context (as is done currently) would make things a lot easier, not just for machines but for people to, the only way to tell currently if ''' is really opening a whole lot of bold text or just opening some italic text is to find the matching '' or ''', that's not intuitive at all.