100percent, sorry I would have to classify both of those concerns as red herrings. Liability to a landowner crossing public to public? Yeah okay. Also as has been pointed out to you already, many states have liability exemptions for people recreating on their land without compensation.
Fences, I agree that crossing a corner with a fence is a problem where that fence meets in the corner. A stile is a simple solution. But fence wear and tear? Common, I've crossed a fence literally thousands of times on public land as have a whole bunch of guys on here. Complete non issue.