Do panhandlers pay tax on begging gains?

The money is taxable. Any money or other goods/services received for a thing or personal service is taxable. That doesn’t mean a return automatically must be filed. AGI has to be more than the standard deduction to have to even file. There are exceptions which make you file even if no tax liability.

Ours don’t, no.

Would you?

Only if they get checks and money orders. Cash money leaves no trail.

Of course not.

There is a minimum threshold, below which you do not pay tax, whether earned income or cash donations.

HA! Good one!

Yes, and bank robbers as well. It is filed as unearned income and needs to be itemized. Mafia kingpin Al Capone was sentenced for tax evasion. Link

On the other hand, maybe the money that they spend is deductible as a charitable donation for themselves.

Under U.S. law, gifts aren’t taxable income to recipients. A panhandler asks for money and receives some from kindly people, without providing any goods or services as consideration. That money is a gift.