That assumes you have control over the callers. If you're writing a library, you don't. Checked assumptions are incompatible with polymorphism and even just basic abstraction afforded by functions. One can't arbitrarily change an implementation without changing the signature and breaking all the callers.

The vast majority of cases, direct callers can't properly the handle the new error anyway. Callers either have to eat that exception, convert it (thus defeating the purpose of checked exceptions), or change their signature. Good programmers will change the signature and now every one of the callers of those methods have do the same thing. Ad infinitum.

You can have multiple implementations of database drivers, but they all throw a subclass of SQLException. So yes, polymorphism is certainly possible. And when you get a SQLException (for example SQLIntegrityConstraintViolationException), you don't want to just crash, or display whatever error message the database gave you... you want to, at the very least, provide guidance to the user on what corrective action to take. And in some cases the program can automatically take corrective action. And that's the reason for writing down a list of possible exceptions where recovery and retry are possible (aka checked exceptions).

That's an extremely contrived example. What if now you want to do a NoSQL solution? Or a flat file?

But really the problem is actually far worse than that. Checked exceptions are brittle under any kind of implementation change. If you have a function that calculates a rate just using arithmetic. But tomorrow it loads a flat file. And next week it uses SQL. And in a month it calls a web service. As a consumer, this is none of your concern -- that's the whole point of abstraction. It's even worse when dynamic (polymorhphism) or functional (external code calls you).

What's the recovery from a SQLException anyway? How does that give you enough detail to do anything? You say SQLIntegrityConstraintViolationException but that's not the same type. Why does it matter that you declared it a SQLException over just Exception in that case?