It isn't? You have a function red that doesn't throws anything you use a function blue that throws checked exceptions you handle the exception and it's all. The red functions doesn't become blue.
if the "red" function isn't successful, than you're mapping that error to what? a RuntimeException? great – you've now escaped the indirection with the original solution – just use RuntimeExceptions.
map it to another checked exception and you now have a "blue" function. and, you also have another layer of abstraction in your errors.
if you can't actually handle the error, skip the circus and just let the exception propagate to a general error boundary (alongside all those RuntimeExceptions you're unaware of).
It's a deep ocean, your defense mechanism of guarding against Checked Exceptions is a small fraction of all exceptions.
To be fair, I did really like the idea of checked functions when I first started using Java. But in practice, it's just too hard to tell what operations should be Checked / Unchecked (sometimes).
