I can imagine that leaving them seperate causes problems.

Take physics at very small scales, for example. Is space-time quantized? Does it come in discrete "packages" or "particles" in a similar way that matter and energy are quantized? If so, then we need a quantum theory of gravity, since gravity is an emergent property of curved space-time. Apparently, there was some experiment not too long ago that demonstrated that neutrons occupy quantized energy states when falling through a gravitational potential.

I think the idea of anything infinite in physics is a sign of a problem, so if we want to think of space-time (and therefore gravity) as being unquantized, then we can imagine a black hole shrinking down to an infinitely small point. It's much "neater" if we can model black hole singularities as having a very small, but finite size (which could once again arise from the assumption that quantization means that there is a "smallest size" of space-time that the singlurity can't shrink below).