I think it would be more pragmatic to say philosophers should find ways to make unfalsifiable claims falsifiable, and that way the scientists could work on them. But 1) this is actually what scientists already do when confronted with new problems, and 2) the statements rests on pragmatism, which is not mandatory unless of course you are already a scientist.

Ultimately any thought can be advanced with further thinking because concepts and ideas are progressive. Our mind is an incredible machine, and for anyone to feel thinking is only for philosophers is truly doing themselves a disservice. We all need to learn to think harder. And our "philosophers" need to find ways to teach how to think better and harder and newer thoughts. What anyone thinks or thought of in the past is more history than philosophy.