Shambles, the tradition of having someone collect for the performer is called 'bottling.'
Much like a barker or shill at a carnival or sideshow.
It is an old and respected tradition that seems to be falling out of favor because of the experience you had in the subway.
When I busked years ago, I had a 'bottler,' a very witty Dubliner who could charm the coins out of peoples' pockets as he passed the hat.
Many times, buskers will use pretty young ladies/wives/sweethearts to bottle for them.
Appearance and attitude matter when bottling, and a threatening mien - even if the bottler is the nicest person on earth - will have an adverse effect on the take.

Seamus