Tips are subsidizing the servers' wages. Servers are "paid" $2.15/hour. The rest of their wages are tips.
We are pretty much in AuntDot's camp. We will tip more (%) at a less expensive restaurant. But in her parameters usually.
I think saying "we decide what it is worth" is just not fair if less than 15%. When going out to eat we all know the customs in the US--the tip is not included and between 15 and 20% is considered to be the norm. If you go to a restaurant knowing you can't meet that criterion then I think choosing another would be more fair.
Servers do have to share their tips and they do work hard.
If service is bad, we tip 15% and write a note on the bill that the service was bad.
All of our kids have been servers and up to managers, including right now. When they are with us we let them do the tip. Those are lucky servers, IF they are good. If not, they get 15%.
If service is really bad AND is the fault of the server (VERY important--they don't control the kitchen) I will tell them in some way.
With regard to taxes, if the bill is in the hundreds, I will take a look at the tax.
Leaving without tipping absolutely requires (TO ME) having told the management of the situation.
I would be interested to know what type of restaurant and if you were completely ignored, the service was slow--whose fault was it really.