I don’t think this is as big a concern as you might expect. I’ve stayed in several expensive but “granola” lodgings that had NO door locks - (both Breitenbush in OR and Deetjen’s Big Sur Inn in CA). The backpacking community might be more comfortable with this than most guests.
Air recently did a profile on a host in Brooklyn with two listed rooms who has no locks on the bedrooms. Her solution was a bank of lockers at the door; guests are told they can bring their own locks. Works for them.