Exactly, the binding is a function of the publisher and there are binding systems that have the behavior the GP is looking for. The rubber binding you've mentioned is fine but it isn't particularly durable (it is how notepads are bound for example.
Sunnyvale used to have an adult education class on book binding that ran during the summer. I still have my class project from that class somewhere (which was a sewn case binding).
All that said, if the paper is stiff then the only lie flat option is spiral or comb binding.
It's got the desirable property of being lay-flat (like perfect binding), but also allows you to make a very strong/durable binding. I'm excited to try it for my next project.
So how long would you expect books bound this way to last?
I took some pictures of the ones I've made for reference: https://imgur.com/a/60zP8vn .
So far, none of them have come apart but I'm pretty careful with my books.
With cheese cloth and library tape? Many years. If there is just the gum on the binding (no tape or linen binding) then a couple of years with light use, less time with heavier use. One of the things that the binding class taught was that books would be rebound several times in their lifetime. I've rebound at least a half dozen paperbacks that eventually started dropping pages (became detached from the binding).
There is an excellent resource on binding examples here: https://www.designersinsights.com/designer-resources/choosin... which goes over them. But since book binding is literally several hundred years old there are lots of good references.
Sunnyvale used to have an adult education class on book binding that ran during the summer. I still have my class project from that class somewhere (which was a sewn case binding).
All that said, if the paper is stiff then the only lie flat option is spiral or comb binding.