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.

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.