I repeat what I wrote above: "busking" is a relatively modern term (chiefly British) for what minstrels and troubadours did in centuries past (and remember, many of the older narrative and lyrical songs that are now regarded as traditional ballads and folk songs came from the poetic and musical talents of these minstrels and troubadours [read The Wandering Scholars by Helen Waddell]). If they were not either lucky enough to gain the patronage of a noble or aristocrat and work in a manor house or castle--or if they did not want such a gig--they would sing in the town square or in taverns or other public places in the hope that those who enjoyed their music would reward them with a few coppers.

It is not begging. It is a time-honored tradition.

Merriam-Webster defines "beg" or "begging" thusly:

Main Entry:   beg
Pronunciation:   beg
Function:   verb
Inflected Form(s)
Etymology:   Middle English beggen
transitive senses
1 :   to ask for as a charity
2 a :   to ask earnestly for : ENTREAT   b :   to require as necessary or appropriate
3 a :   EVADE, SIDESTEP (begged the real problems) b :   to pass over or ignore by assuming to be established or settled (beg the question)
intransitive senses
1 :   to ask for alms
2 :   to ask earnestly (begged for mercy)

Wikipedia offers the following definition:

busking is the practice of performing in public places to receive donations [emphasis mine] of money. The performance is often musical, but juggling, comedy, and sometimes magic is also displayed.

Note the word "donation." A donation is a gift, or contribution, as in "voluntary contributions will be accepted with thanks." Many long-lived and well-respected institutions and services survive by voluntary contributions. I leave it to you to make your own list. It's quite educational to do so (e.g. do you go to church? Watch public television? Listen to public radio? Drop a few coins in the can beside the cash register for breast cancer research? Uh--support your local troubadour?).   

THIS should settle the matter once and for all.

Busking is most assuredly not begging.

Don Firth