Generally they are not really "cheap", as most of those non-tipping European visitors to the US are paying on average substantially more for the included service costs in their home market.

The reason that the US has the tipping culture we do is because the government allows so many employers to pay so many employees with sub-standard base pay and tell the employees that they may make it up with the variable pay element of tips, which customers may or may not provide. For employers, this creates a more flexible labor market. Whether or not tipping leads to better sub-employed employee performance overall or not is secondary to the financial benefit to business interests in being able to shift the risk of poor market demand for business services onto the employees of the business.