Fundamentally, the problem is that whether an exception should be checked or runtime depends on the context. It makes no sense so say that "FileNotFoundException" is checked.
If that exception is thrown because a user selected a file that disappeared, it's recoverable, so it should be checked.
If that exception is being thrown at startup because the app failed to find a file that absolutely needs to be present otherwise everything is broken, then it should be runtime.
Obviously, Java will never be able to adjust to that perspective on exceptions since it would break pretty much everything.
I completely agree that context matters immensely and ultimately it's the caller rather than the callee that should decide whether an exception is fatal.
FWIW though I think that Java the language could adjust to that perspective, if nearly all current exceptions were checked exceptions by default and then callers were expected to wrap as a RuntimeException (perhaps something that was a bit more suggestively named such as FatalException) whatever exceptions they deemed unrecoverable.
Unfortunately there's some implementation-specific problems of going that route (generating exceptions is expensive and you'd probably want a far more fine-grained exception hierarchy rather than lumping whole classes of things under say generic IllegalArgumentExceptions), but they don't seem insurmountable.
More importantly though I agree that I doubt Java the community would ever accept that, at least not for a long long long time.
I suspect the proportion of Java programmers who like checked exceptions even in principle is decreasing over time unfortunately. So waiting might just result in it never being implemented :/ (although I guess that's probably a point in favor of waiting and never expending the wasted energy).
Just looking at the developments of past decade the community seems to be going hard for all exceptions being unchecked. Other statically typed JVM languages (Scala and Kotlin) advertise a lack of checked exceptions as an improvement over Java. Various Java plugins also tout the ability to remove checked exceptions. Manifold is particularly exuberant about it. Lombok offers this capability but is much more reserved about it, in no small part because the way it does so has pretty big downsides.
It's a bit sad (from my tiny personal perspective) because checked exceptions in Java have some ergonomic benefits over Result/Either types in other languages, but social dynamics are what they are.
I meant future releases. That people can manage now make the problem not one of extreme urgency, so we're waiting until there's a solution we like.