I ask for a deposit of a mobile top up voucher if someone has previously not turned up without explanation. I always explain why to the client.
I wouldn't ask for one as routine though.
Contract phones can easily be traced.
PAYG phones can be traced quite easily if they have been purchased or topped up with credit / debit card.
and yes you are right, although there is no actual name attached to the phone if you buy in cash, don't register, and top-up in cash, they can still be triangulated to a quite precise location, but the police would only bother with that if it was a very serious crime.
I never answer witheld numbers or payphones as they are usually no-shows or last minute cancellations . Also for the reason that it could more easily be someone I know has seen my pictures (no face sorry Jimmy haha) and wondered "Is it her?" . My ex boyfriend found me on AW a few years ago when I only had one picture from the back with underwear on (and showing hair obviously) - I recognised his number calling the work phone after a spate of "withheld number" calls I ignored. If I had answered he would have been surer that it was actually me from my voice. Afterwards I got texts to my personal phone with links to my AW profile from him. He has since moved abroad thank god. Obviously someone clever would just use a cheap £5 sim or a mate's phone but I don;t think he was that clever