I've learned years ago that even the "interesting" things have little chance to happen if they cost money. While visiting one of the most interesting caves in Poland the guide said that geologists strongly suspect that there's an entire tunnel system underneath it, and have suspected it for 40-odd years. So I asked - well, it should be fairly easy to check with the right equipment, no? And he said that yeah, it should be fairly easy, and even though multiple universities expressed interest in doing it, no one is willing to cough up the money for it. I guess this is very similar - of course it would be extremely interesting to find out where that water is going,but redirecting the flow of water would be very costly, and apart from satiating some scientific curiosity there's little reason to undertake such large engineering project.
Just tell them you think there is a train full of Nazi gold in those tunnels :-). Something we don't have enough of these days are "gentlemen explorers" folks who are independently wealthy and spending their days exploring interesting places.
I had a similar experience here in a shallow cave in Texas. When you reach the 'end' you really just reach the point at which the cave is flooded. The cave has been well known for over a hundred years and likely goes on quite a ways. No one really has an interest in exploring it. It'd be an expensive and likely just discover a bunch of rock and water.
With respect to cave systems, it seems like that the key is finding a previously unknown species. Or find a species in the cave that was thought to have a very limited distribution.
I bet you could do something neat with small tethered submersibles that you remotely control. Of course, they might not be small enough, but at least it would be safer.