>I'd much rather send feedback to the managers. They control the entire experience.

It's a very naive view not only of restaurant operations, but of the human world as whole.

>Are there any restaurants that pay management $2/hr and let the customers tip them up to living wage levels?

This is an interesting question which has no relation to tipping. It seems that in the US tips make most of what server earns - it's not the rule everywhere. However, I'm not in position to judge which way is better (e.g. where a good server really earns more).

Nevertheless, money paid to servers come from customers, and you have to pay more if you want to make servers earn more. It can be called "tips", and be a choice in a range, or it can be hardcoded into prices (with some administrative overhead, of course). I'm not a fan of administrative overheads, but YMMV.