Price(A) > Price(B)
=>
B > A
--------------------
Simplification aside, tipping is a service as well. The tipper "feels" good about tipping, the same way people donate or buy because of donations when there are such campaigns. For a lot of people the utility of that is close to 0, so they don't tip. For some its very high.
So it makes sense to have tipping as a way to implement price differentiation.
This would be true if tipping was optional, rather than expected. But this isn't even close to how things work in the US. In the US, you tip so that the restaurant can advertise lower prices on their menu. That's it. They tell you a burger costs $12, when in reality it costs $15. And if you decide to only pay $12 instead of $15 the restaurant just makes the waiter eat the cost.
Price discrimination means you can sell at a lower price to customers who might will not buy otherwise.
There is no price obfuscation.
I think in a world where people made enough money to eat and we didn't outlaw the stupid penny, we could keep all the pennies and offer them to people as tokens of our appreciation, then it's operating as a symbol and the emotional purpose is served without people who don't want to tip feeling expected to support people's lives all of the sudden at the end of the meal.
Our current system makes thoughtful, considerate people feel guilty if they don't want to tip deep down but feel they ought to.
Steve Martin's My Blue Heaven deals with the problem of wanting to express gratitude and joy to people in a world where everything is officious and transactional