There is a KYC free alternative to local bitcoins. It's called Particl marketplace. It's an anonymous yet trustless marketplace (particl.io). You can pay for any goods or services there including bank transfers, there is someone listing monero for sale there currently, but you can also get bullion, cash in the post and bank transfers.

Pparticl also has a fully decentralised and trustless cross blockchain atomic swap exchange (basicswapdex.com). The developers are currently integrating the exchange directly into the marketplace so that you can pay in pretty much any cypto. So it's not so much a local bitcoins replacement as an "any crypto" to fiat, bullion and cash in the post replacement.

The exchange is proving very popular with the monero community who have been extensively testing it and are considering including it as a pluugin with their default wallet so any monero user can access the exchange as well.

Here is a neat video on it: https://youtu.be/1gYNX4ue_O4