One possibility: Interstates are big roads that make it faster to get somewhere you could get on another road if you didn't mind going slower. Some (esp. rural) roads with 45+mph speed limits are the only way to get somewhere, therefor bikes need access. Anyway I'm also just waxing; I don't know the exact laws and surely there are exceptions- generally speaking "all but Interstate" seems like a reasonable thumbrule.

There are places not accessible by roads with bike-accessible speed limits. Those are much more common than places not accessible except by interstate. (Incidentally, biking on the shoulder of the interstate is permissible in my state, with the occasional exception of some cities and bridges without shoulders.)

I'm not sure I follow the thrust of your comment.

I am interested in why sequoia asserts that it's correct (or at least permissible) to prohibit bicycles from interstates but a violation of rights to prohibit them from other roads. The fact that bicycles are not prohibited from all interstates seems somewhat orthogonal...

I think it's reasonable to designate certain very-high-speed roads as "car only" when there are reasonable alternative routes for bikes. If there's a destination you can only get to by interstate I'd say "allow bikes." I'm a biker and strongly pro bike-rights but I recognize that certain exceptions are reasonable for safety & expediency. :)

So hypothetically, you wouldn't object (on "rights" grounds) if there were a non-interstate that was labeled no-bikes when there were plenty of alternate routes to everywhere serviced by that thoroughfare. Sounds reasonable to me.