That's good idea at the same time not really good idea. I think the uses only fit for small - decent transaction not recommend to use for big transaction.
I'm interested to p2p trading system. You said above bot become an escrow, how the buyer(who transfer fiat) transfer the amount?
Yes, sending big amounts is not recommended, could be fine for day-to-day cash. Admit it, nobody is using localbitcoins as a wallet too.
Buyer will transfer fiat as agreed with the seller: bank transfer, cash deposit, face-to-face or any other way both sides find reasonable. I will show some warnings for bank transfers and paypal, that transactions are reversible, be cautious and don't trade with strangers.
Okay that's good options.