I don't remember going to a RTE like you described although maybe I have. Pretty much all of the RTE's have a spot to meet. Then the group rides to the eat spot and eats. There is normally a ride back after eating but often some people break off and ride home by themselves. It is also common for some people to skip the ride and meet at the restaurant but typically most people don't do that.
I'm not saying that there aren't lunch rides like you describe, it's just that I don't see them very often. Most of the people I ride with like to ride with others. If they didn't I probably wouldn't know them because they would never come ride with me.
To clarify what I am talking about because I think we have a difference of terminology.
Many of the rides I see posted on FB or forums will have a title of: XXXXXX restaurant lunch ride or something like that. When I post a ride I will say some thing like: Dual sport ride" or "Street ride". then I'll post where and when to meet and describe the ride. After all that I'll mention where we are likely to eat but won't post a time because we'll get there when we get there. It's about the ride, not lunch.
On the other hand when I see what I consider a RTE it will have the time and place to meet, the restaurant and say little or nothing about the ride. In some cases these groups ride together often maybe they don't really need to talk about the route. My rides vary greatly so I do include things like what types of bikes are suitable for the ride. I don't want a beginner on a 550 pound adventure bike to show up to ride that would be over his head.
As for riding groups, my experience has been very different than yours. I have had around 99% positive experience riding with groups but I do stay away from certain types of groups.
We come from different backgrounds of riding. The concept of group rides projects a local group of riders getting together for a ride. My 'local' was the entire North American continent, so riders for a RTE in CA might come from MA, FL, OR and CA, along with any possible other states and Canada. When you routinely cover 1k or more a day, getting together for a group ride isn't really a thing. When my Beautiful Wife and I would get together with the local moto group in St George, UT it was always a running joke that "here's the route, we have a couple of choices for lunch that we'll talk about later, and Cletha and Eric will probably detour through Seattle and meet us there." 😁 Different focus, still fun with the right people.
We are defining things differently. What you're talking about are group rides. RTEs are group rides in some circles, completely not in others. Personally, and yes, it's just me, the term RTE is corrupted when used to indicate a group ride. As you correctly indicated, it's not Riding To Eat, it's a group ride that happens to have a planned lunch stop. No point in calling it a RTE. And you would be bored by the riders that just wanted to ride strait to the Eat location via the most direct route.
The UK guys use RTE in reference to an event where the focus is on discussion and sharing info about riding while at the selected lunch location, but riders still follow their own paths singularly or in small groups.
Now, I do know some guys that Ride To Pie and are
serious about the pie! They may or may not ride in a group, varying on the pie location, but it's all about the pie.
Our prime difference in perspective is that you ride local with others, while I never ride local with others. Nor do I want to. I have in the past, but with mixed results. Unless it's the same small group of riders that know each other and how they ride, I'm not really interested. The other issue I have with group rides is the number of people that won't think for themselves and expect someone else to plan the route and lead them along. Not the kind of riders I'm used to being around. This is why we don't share opinions when you propose a ride.