I get that it goes against the fundamentals of crypto currency, but exactly for what reasons though? Assuming you're not using it for anything illegal (if you are then it's understandable), why the concern? I'm asking specifically when trading.
The major concern is always an identity theft, however considering that you are using a smartphone and a carrier your data is already being sent to many tech companies and hence your identity has already been stolen to some extent.
Dont rule out the "illegal" scenario just like that. Majority proponents of the no-kyc trend are done by criminal groups and who are into money laundering and I am not talking about your average street muggers, these are bigger corporations who are investing in cryptocurrency and own money that they have obtained by illegal means and trying to offshore it using bitcoin's pseudo-anonymity and lack of taxation.
Again it does not go against the ideals - when you are using someone's exchange, you are bound to be their terms, you like or not. Otherwise just go to OTC markets and exchange, but dont ask for safety concerns, liquidity and availability over there.