How do you think of that?
if the users wanna be anonymous they can buy bitcoin on localbitcoin.com paxpul.com
and they can use bitcoin mixing service are like bitmixer, cryptomixer and other bitcoin mixing service.
localbitcoin anonymous, i don't know a single btc trader on local bitcoins that doesn't ask for full Verified ID to trade any decent amount of bitcoin.
add to that the crazy level premiers buyer and sellers charge kinda makes bitcoin pointless to average joes.
and you meet them on local area and pay with cash money or bank transfer, it will not needs ask for full verified your identity. I don't know what is mean localbitcoin in your mind, in my mind localbitcoin we buy bitcoin from the sellers in one area.