I think that clearance for getting things like a colander in the sink is the reason for the higher arc faucets.

The overal depth of the sink is important as to splashing.

I wish I had selected a faucet for mine that could accept a Pur faucet filter. Not sure if you would use that but it is something to consider.

Bathroom faucets usually have a much shorter reach than kitchen faucets...so I would think it would not work well in the kitchen. You say you have a small prep sink...how small is small? What are it's interior dimensions?

We have a small prep sink and put in a pull-out faucet rather than a pull-down/high-arc faucet. Our sink was too small, IMO, for a gooseneck or pull-down faucet plus since our prep sink is in the corner with the peninsula, I didn't want to focus on the faucet.

We did put a high-arc, pull-down faucet at the cleanup sink.

In retrospect, I think the decision to go with the two different types of faucets was a good decision - I have the pros of both and none of the cons b/c I use the faucet that's best for my need at the time!

My prep sink is 15-3/4" square: