There would be great benefit and could be the objective proof of whether the dominating theories about the nature of a black hole are correct or incorrect.
You can 'prove' any number of things with logic but it doesn't make them necessarily true because you could easily be missing a crucial element of evidence in your deduction/induction. We see this happen all of the time, even though mathematical proofs are logically flawless.
As such, sending a probe in would be able to demonstrate the validity of proofs or lack thereof. If we never hear from it again then we have objective and tangible evidence to weigh in support of the singularity theory, as well as the theory of infinite compression of dimensional matter and space.
For example, you can posit with equations that jumping off your bed will pull you to the floor but you won't know for an absolute certainty until you do it.
Theoretically your bed is the only place in the universe where gravity exists.