I have self conveyanced a few times. Even during covid (aaaargg) and money laundering but was never an issue.
Broadly there are three bits :
Selling bit - hard details part of self conveyancing.
Buying bit - easyiest apart from dealing with the arrogance of another parties solicitor.
Impossible bit. Self conveyancing is not possible if there is a charge involved (mortgage). Few people realise your lender instructs your solicitor to act for them. No solicitor no mortgage.
Money laundering laws are a combination of a few acts (proceeds from crime and some financal acts). Solicitors interpret they how they use them and ime they range from "propper pain in the ar3e" to "if you say so".
A mortgage with "Free sols" are normally the absolute worse, pretty much cos they're is very little solicitor involvement. No really.