The BBC article's "sales tax" reason sounds good - unless you know that several US states do not have sales tax.

The actual history of tipping: https://en.wikipedia.org/wiki/Tipping#History

And a bit on Sales Taxes: https://en.wikipedia.org/wiki/Sales_tax#In_the_United_States

From old family stories, I figure the real reason for tipping service workers is that both employers and customers want there to be plenty of service workers available - but the demand for their labor (restaurant customers, whatever) is very unpredictable compared to factory, farm, or gov't work. And service industries can't afford to keep a lot of idle workers around at full pay. So tipping is a simple revenue-sharing scheme, wrapped in social niceties, that boosts/cuts the service workers' income based on whether business is currently fast or slow.

Even in the majority of states that have sales tax, services are exempt and voluntary tips are also not taxable. (Mandatory tips are often considered part of the sales price, which seems reasonable enough to me.)

True. I live in a no-sales-tax state but we have just as much tipping as everywhere else.