Others in this thread have suggested that the restaurant give locals a 'locals card', which would allow them to purchase food at a more reasonable price.
Several of the local places do "frequent diner/visitor" loyalty cards, where the 5th or 9th meal (for restaurants), coffee (coffee shops), etc are free. This offsets the otherwise high prices charged on menu items.
Also, once a year (during the off season, of course), the local high school sells a booster card that gets a percent discount off for the entire year at numerous local places.
This is of course not unique to a touristy area, but I find myself using them far more often than in other places I've lived.
Any person travelling just coming by for the "best burger" probably would not want to spend $34 and not use that card anymore so $20 sounds great. Any regular would probably be super cool with paying that extra $30 knowing they can get a burger once a week or whatever for $4. This works out for the restaurant and the regulars, and like you said they can just hand out those cards to anyone for any reason.
Plus having special cards feels corporate, not homey. Looking at an ID for locals discount is pretty well trodden ground.
There are already markets for fake IDs, so unless you're suggesting that small local restaurants purchase scanners to confirm the authenticity of each ID, it would be relatively easy to circumvent this check too. (Some states require IDs to be scanned for selling alcohol, but many, e.g. in Oregon, do not, and the only check is some employee looking at a card in their hands for a couple of seconds)
> Plus having special cards feels corporate
Not at all. Plenty of local restaurants in my are (Portland, OR) have rewards cards, where you get stamps and a free meal after some amount of stamps.