However, if you bind it yourself, you can get the desired behavior pretty easily.
I have a summary of my process in the footnote of an older comment, but I've been able to get it working with hardcover books, and experimented with using a little bit of thread to reinforce the binding.
So far, none of my books have come apart and they all lay flat.
The problem with this is that you either have to print your own books or remove the binding from existing ones and then rebind them, which is not especially time consuming but not exactly fast either.
I wonder why this style of binding isn't more common?
Is it just too expensive or are there durability concerns?
Well done. :)
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.
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.