cutting down 1/0 to 4 gauge?

Do that and you've turned the 1/0 wire into a 4 ga. wire.  It's akin to the saying "A chain is only as strong as its weakest link".  If you reduce a wire at the end by trimming strands, you are in effect reducing the gauge of the entire length of that wire.

Show me an amplifier that pulls so much amperage it needs a 1/0 input.  If you have such a beast, run a dedicated 1/0 from the battery directly to the amp (assuming the amp is capable of an input that large), and another wire to the distro block to feed the other amps.

Let's look at some numbers:  see https://www.the12volt.com/info/recwirsz.asp  (Those are RMS numbers, not max or peak.  The recommended wire sizes allow for the peaks.)

If your sub amp is pulling more than 150 amps, you need larger than 4 ga. wire input.  If it's more than 225 amps, you need larger than 2 ga. wire.  Look at the amp's fuse rating to know the answer.

I agree - the only thing that requires 1/0g direct is an arcwelder.  Unless your amp can do that, there's no advantage to having that firehose going into it. 

I don't thnk, however, that there's any appreciable loss from trimming down a 1/4" where it enters the distro block, and would seriously doubt you'd ever hear the difference.  That's like saying a pin connector on 10 guage speaker wire reduces that entire wire to 22g.  (Entire wire, I like that.)

If I'm wrong about that please correct me, as I'm just theorizing.