Direct answer: Limit yourself to less formal restaurants, which operate in "cafeteria style", where you go to a counter to order, and are given a pager to come collect your food, or a tent card to put on your table and a runner delivers it. (that's the last you'll see of the runner). These are becoming surprisingly good, that is to say, the food is good. The demographic is middle-to-upper-class, who want an upscale taste without the time and expense of waitservice. Panera Bread, Noodles & Company, Chipotle, Qdoba, Mod Pizza, Smashburger, various Korean BBQ, etc. As well as a variety of locally-owned one-off or mini-chains (Buckhorn, Firewood Grill).
Not to be confused with waitstaffed, must-tip restaurants going downscale by offering plain cheap food but retaining waitservice formalities (and thus the obligation to tip): Denny's, Steak & Shake, Cracker Barrel, your local greasy spoon diner, etc. These places are for people who want to be pampered on a budget, but want plain food that appeals to their palate. In these places you will be seated, a waiter will give you a menu and listen to you give your order verbally, and that means you need to tip!
You can also consider plain old fast-food, like McDonalds, Taco Bell, Wendy's, Burger King, KFC, Arby's, Subway, Sonic, Hardees/Carls Jr, Tim Hortons, Whataburger, Del Taco, White Castle, most pizza places, etc. Their hallmarks are lab-engineered food design, industrial food sourcing and distribution, lousy ambience, salt-of-the-earth clientele, cheap pop music (Muzak), frazzled minimum-wage staff, etc. To get the genuine American experience, make sure to be one of the 70% of customers who orders through the drive-through.
I thought the upscale-cafeteria type, such as Panera Bread, was referred to as "fast casual". But Google thinks otherwise, a search for "fast casual" will turn up 95% "plain old fast food", so that's useless.
If you genuinely have a medical need that requires you get waitservice, focus on fast-casual restaurants and request the staff help you. There is a disability-support law called ADA which obliges them to do what is easy.
Other than that, if you're a waitservice snob who insists on the formalities but can't tip, that is incompatible with being on this continent. That thing doesn't exist because the culture here is so strong, and you can't flip that culture, it's certainly been tried. I am not here to troubleshoot your issue with tipping but to say it may be troubleshootable, feel free to ask a separate question.