I don't know about Paxful's KYC policy, but their volumes seem to be starting to decline too, according to
coindance and the current weekily of $30M is nowhere near Localbitcoin's all-time high of over $120M weekly trading volume.
Don't dwell in the past glory, you can't use all-time success to judge the stability and suitability of any business. The all-time high I even read was in 2017 and it's $130M but that is not the case here. Yahoo was doing better than Google some time ago, but can you compare the two in earnings now? Paxful was a better competitor and traffic trackers ranked it #16,947 while Localbitcoins ranked #42,159. That should mean something to you.
The lost the volumes so quickly because of their strict KYC policy and they suffocated so fast.
I don't think so, if they lost due to KYC, why are the others with the same KYC flourishing in the business? What I have noticed is that businesses with their model accepting all manner of payment systems for P2P need due process to protect themselves and their customers because fraudsters are everywhere.