This varies by state. For example, in Oregon the minimum wage is $9.75, and, importantly: Oregon is one of the few states that does not allow employers to take a tip credit. Employees must be paid at least the full state minimum wage, whether or not they also earn tips.
Despite this "high" wage, there is no shortage of restaurants in Oregon. Somehow good restaurants do manage to stay in business here.
http://www.nolo.com/legal-encyclopedia/oregon-laws-tipped-em...
In the USA, all tipped employees always earn at least the federal minimum wage. There is no such thing as a service worker making $2.35 per hour.
https://www.dol.gov/whd/regs/compliance/whdfs15.htm
It's possible that food service workers might earn a lot more than minimum wage with tips, such that taking away their tips would hurt their compensation. Perhaps - it's still arguably no concern of the patron. If I'm buying an automobile from a car dealership, should I pay extra because the poor car salesman needs his commission? I don't think so. His compensation is between him and the leadership. It is fair that I negotiate the lowest possible price, and a price that works for me.
Regardless of all that, my primary point is that it is incorrect to claim that servers will make less than minimum wage without tips. They always earn minimum wage and so this is not a reason to justify tipping.