So your question is backwards because local dealers had a working solution for their business, but "startups" like lieferando destroy that just to sell and control their own solution. So now the domain is worthless, but only because of lieferando et al.
The same happened to booking hotels. Now every hotel room is 20 to 30 % more costly because booking.com forced themselves between the business and the customer and they take their cut.
doctolib is trying to do the same with doctors in europe.
As a restaurant in a situation like this, you now have to compete for the search results, which isn't your main business. You want to sell pizza, not do SEO, or SEA. And then lieferando calls and tell you something like "hey, it's a shame that nobody is buying from you, right? Well, we can help for 10% of your revenue..."
- kaiser.restaurant is free - restaurant-kaiser.com is free
5 seconds of work, both probably better than gasthauskaiser.de tbh.
It totally does and it's not mutually exclusive with a social media presence. And now that many people are using LLMs also for searching, if LLMs do redirect to your domain it's bingo.
There's this fantasy that people only ever use their phones and social media and that computers do not exist anymore. Then there's the real world where people actually work and they're all on real computers and they do look stuff in either good old search engines or using LLMs, by typing on an actual keyboard and looking at the results at an actual screen.
If you're showing food recipes or Minecraft vids: fine, your social account will do. But for anything related to the real world, where real people doing real work in actual offices may be looking you up, a domain shall greatly help.
In addition to that: many people at work are also using their actual computers to look up personal stuff. Looks more serious to do it at the computer than on a phone.
And as as been pointed by several in this thread already: at least its a presence you can control without being at the mercy of a single company.