As far back as I can remember they’ve used these warming trays to keep items that were previously grilled warm until someone orders them. This is pretty much required for fast food with the volumes and wait time people expect, otherwise you’d be waiting 5+min for your burger. 
Thank you for specifying that you’re not technical, that helps. Your idea doesn’t make a lot of sense since you have a misunderstanding of how the Internet works, and at which levels the problems occur.
The first layer of the “Internet” is physical infrastructure. The router you mention, the ISPs you connect to, etc. All they do is move data around the world, mostly without a care to what that data is, and they do it VERY effectively. Apart from pricing or service you might not like, there is no need to replace this part of the Internet because it is by far the most expensive and complex component, and has little to do with the problems you lament. Setting your own version of this up would be vastly inferior, more expensive, and very unreliable.
The second part of the Internet is the protocols and standards used to get this data around on the physical fibre and wires that the ISPs have laid down. Again, these protocols are time tested, mostly content agnostic, and highly compatible. Things like routing protocols, HTTP, DNS, etc are all open and free to use.
The third part of the Internet is the millions of servers that actually hold the content. This could be web servers that show you the web page you’re browsing on, servers that orchestrate instant messaging, the backend to your apps, etc. This is what you seem to have the biggest issue with and it’s also the easiest (relatively) to replace.
So, now that the basics are down, let’s discuss what you want to do. You want to have your own Internet that’s seperate from the one you see. You could do this as simply as getting some people together who are like minded, making some web servers to host the things you want like a Wikipedia clone, email server, what have you, and then and then use a DNS server that only resolves your new servers and does not return results from the broader Internet. Think of a DNS server like a phonebook for computers. If you make an exclusive friends club and print your own phone book and pass it around, but forbid anyone from ever looking at the local white or yellow pages, your little group is all they’ll know but they can still use the existing telephone system.
Most protocols are encrypted these days, so your DNS and web browsing can be fairly anonymous if everyone conforms to a set of standards. If you want more you could set this whole thing up over a system of VPNs.
Long story short is, big mesh routers are just a bad idea for so many reasons that I haven’t even gotten into like RF spectrum use and maintenance. You’re better off participating in small corners of the existing Internet you enjoy (like Lemmy or other alternative sites) and ignoring the rest. If for some reason you really felt you wanted to make a Dark Web 2.0 for like minded people it can be done, but I wouldn’t start by cutting the cable to your ISP.
I largely agree with what your saying that fast food should be saved for travel or times where the time/convenience is necessary, but can you go into your rationing example? I’m having trouble visualizing a situation where I would need to ration the food I have at home and instead of replenishing it would buy more expensive fast food meals.