People only "have" to tip because our laws allow for there to be less-than-minimum wage for servers. If, just like you imply, this would not be allowed, then tipping wouldn't happen (or at least it would not be required to be able to earn a livable wage).

Your logic is fallacious in that people desire these low paying jobs. Assuming the purpose of a business is to maximize profits, they would want to pay the least possible to any employee, especially a server that can be easily trained and easily replaced. Therefore, if a law allows there to be such low wages, it is not necessarily the business's fault for using the framework that exists to its advantage.

The only reason people "want" those jobs is because tipping can be good but that is certainly not the case with every restaurant, and certainly not most places. Those stories of horrible tippers are more common that you imagine. Even still, the average hourly wage of a server is not that much greater than minimum wage and you can imagine the amount of effort they have to put up with because they have to "earn" their tips (i.e. rude customers, busy days, competition among fellow servers). Some more info: http://www.bls.gov/oes/current/oes353031.htm

In addition, sometimes these server positions are the only ones available to unskilled laborers. Surely you cannot assume that people want these jobs because they are the better opportunity? Being a server is a job that does not require a large amount of prerequisites (such as degrees or certification). It is easier for those who either never had those opportunities or who are struggling and need to make some money. It is essentially, a gamble and no one likes not having a secure wage.

Regardless, tipping has become custom in the US. So even a law guaranteeing a high enough minimum wage will not eliminate tipping, though it might definitely change tipping habits and tipping amounts. Frankly, I do not see that happening any time soon.