I do not like to see people using P2P for centralized exchanges. The centralized exchanges has been confusing people about it. P2P means the exchange should be without any intermediary but the exchanges are the intermediary which make them not to have P2P but another thing entirely.
Yes, P2P simply means peer to peer, and their use of P2P services in their exchanges goes against the definition of P2P. Someone who is well-versed in the crypto industry and often uses exchanges will not be perplexed by what it implies and will understand what the exchanges are referring to. However, a newcomer using a centralised exchange for the first time will only notice that if they are really smart and know what they have learnt about it previously, as well as the meaning and how it works better. It would be preferable if the P2P working principle followed what it means, but an escrow mechanism (the exchange) makes it more trustworthy than simply exchanging through a random individual you don't know.
What about CEP2P? It means centralized exchange P2P.
Why not just scrap the P2P name, so that we all know it’s not a P2P service anymore.
If anyone advertises P2P when it's not, it should be illegal. I have no idea what type of P2P you are talking about but most of the centralized exchanges I know does a P2P keeping itself as an escrow system. Having an escrow in P2P don't make than non-P2P.
Exchanges advertises P2P, which does not portray what P2P is, yet it cannot be considered unlawful because it is the means that brought the two parties together to trade funds. It's even safer and more transparent to use a system like that when trading funds online.