Cake is open to anybody and everybody, sending and receiving, without restrictions based on depositing, etc. I've had very few problems on Cake skins. They do have playthrough requirements on P2P funds received.
Yatahay allows P2Ps (at least ACR does), at least receiving, not sure if there are restrictions on sending.
Last I checked, Merge restricted my right initiate P2P because I hadn't deposited, regardless of whether I had provided any verification documents. I could still receive though. Haven't tried it in a while.