If the restaurant does not require the customers to tip in the same manner that it does for them to pay the bill then the servers should definitely be paid the hourly minimum wage. One possibility, and I believe this is the case in some places, is that whatever amount the server makes in tips is subtracted from the paycheck. So like, if the minimum wage is ten dollars an hour then if they work full time then they should have a gross income of of 400 each week. If they make 200 dollars in tips then their paycheck would consist of 200 dollars and if they make 400 dollars in tips then they wouldn't get a paycheck at all for that week.
Servers should be paid minimum wage plus tips. Servers work very hard for very little money as the system is currently established. Their only way of improving their quality of life is to move to a higher paying job where tips are larger. Those establishments have a very low turnover so it is difficult to move up in the server industry. Restaurant owners are practically getting free work from their employees because they are not required to pay minimum wage.
I have been a waiter and there are days you don't make a dime. Its not fun, The biggest thing is that at the end of it you make your wages, which is always a nice boost. I think on slow days if I didn't have those wages I would quit.
Serves should get the federal minimum wage and tips. The company should be required to pay workers and not depend on customers to do it. Not everyone tips, and if they do it may not be well. Servers also have to split tips at times, or do prep or other services in addition to just serving. They deserve to get the same federal minimum wage that applies to all other workers, and if customers want to tip in addition then it's even better and makes for a better job with better employees.
If servers suddenly started getting a federal minimum wage, they would be less reliant on tips for their income. This would make them care less about pleasing the customers, which would make eating out less enjoyable. Those businesses and even the larger economy would suffer as a result of this change.