Why does America have tipping?

Back in the days of Fifty Questions, a loyal MR reader asked:

I am interested in the economics of tipping.  This seems appropriate, since you seem to eat out a lot.  Why in the United States is the pay of waitstaff structured as it is as compared to elsewhere, where tipping is less expected? 

The best way to understand tipping is to go to a restaurant you will never patronize again.  Once your meal is over, when she is not looking, leave your tip not on your table but rather on another table she served.  That way she still gets her money and you have in no way ripped her off.

That is psychologically tough to do.  You fear the waitress will think you are a lout and a deadbeat.  Of course in no-tipping countries, or for that matter non-tipping sectors, this dilemma does not arise.

The real question is why America is structured so that waiters and waitresses can sell feel-good services ("you are a generous tipper and a fine man") to strangers, in return for money.  In other words, how did waiters end up as fundraisers, noting that the final Marshallian incidence may lower their wages by the amount they receive in tips?  Most cross-cultural explanations of tipping start with the agency problem between diners and servers ("can you bring my drink now?"), but I believe that is the wrong approach.  I view tipping as correlated with effective fundraising in other areas, and Americans as being especially willing to set this additional fundraising arena in motion.