There are many who do. There are many who don't and among those who don't they can have pretty strong opinions and be fairly influential (see e.g. Robert Martin's Clean Code). When I say controversial I don't mean that as a back-handed way of saying no one likes checked exceptions, I mean that to say there are large contingents on either side. Unfortunately that means practically speaking checked exceptions lose a lot of their power since you have to proactively rewrap and rethrow a lot of your underlying libraries since
a lot of them eschew checked exceptions (e.g. big examples that can pervade entire codebases are Spring and Hibernate). That's not impossible to do (I've done it for personal projects before), but I've never had success in convincing coworkers to do it and you're at the mercy of the accuracy of the documentation (or just seeing it blow up enough times).
I was thinking of the fact that the array can be dynamically sized as not being up to the program, but it's certainly true you can ensure the array isn't out of bounds (just check the array length in a single-threaded context or lock and then check the array length in a multithreaded context) in a way that's not possible for files.
Perhaps a more blurry example is ParseException (checked) vs DateTimeParseException (unchecked). I'm pretty sure I know the reasoning behind it, which is that ParseException is thrown by methods that directly ingest user data whereas DateTimeParseException is presumably not and is probably meant mostly for hard-coded strings. But there doesn't seem to be any real distinction between the two cases; it seems reasonable enough to parse strings passed in by the user as datetimes.
When you solvable, I'm curious do you mean currently in Java or with future features? Because right now if I want to play nice with checked exceptions and lambdas I do an ugly thing of wrapping the exception in a RuntimeException, then catching the RuntimeException, downcasting the wrapped exception, and rethrowing it. It'd be nice to know if there's a better way than that to use.