Yes, p2p trading is cheaper but it's also as said by others, riskier. Plus, most wouldn't even bother buying like such since most are actually into trading instead of using it/hodling. There's also the issue of never-ending changing prices every minute, though unless a huge dump occurs, the difference shouldn't be that huge. Transactions may be slower, but honestly, it's just a matter of organizing the transaction. If you, the buyer, were to prepare beforehand some of the issues to be talked about, such as escrow and the like, the time shouldn't be that long, though it would still take longer than using CEX normally.
Edit: oh you are talking about local bitcoin type exchanges. They are highly risky and too slow. They should be and are used only when a person wants to sell crypto for fiat. And that fiat pair isn't listed anywhere. Wazirx in India allows fiat withdrawal in this way but the prices are really on the CMP you can expect a variance of around +/- 0.5-1% at max in rarest of cases
Well, it depends on how you work around it. With escrow and a bit of time to organize, it should be rather easy though it really isn't the best way to buy, especially if you're trading. But if you're just hodling or using it for your own, trying it out may prove to be useful since it guarantees complete anonymity.