> I've gotten explicit permission to cut through when I'm walking my dog from the neighbors that own the most valuable shortcuts, but I wish there were a custom or law that covered this instead of needing to rely on the kindness of strangers.

If enough people cross their land over a long enough period of time (varies by jurisdiction) without permission, that creates a "prescriptive easement," which is essentially what you're asking for. Some decent info here: https://en.wikipedia.org/wiki/Easement#By_prescription