Possible, but perhaps not the best idea. I had a similar idea about the drink silos recently. I imagined that some might want to make a public juice station, where everyone could come and get cups of juice, but not buckets. Perhaps even rate-limiting to x per day or such. I eventually decided against it and protected the purge button only. The purge button allows anyone without any special item, to remove all the work you’ve spent making the juice. All other options require either glass or steel, which isn’t something you can get until you actually do some work. This means brand new players cannot drain the work you’ve spent. For a bed, this is even less of an issue, since the primary function of the bed is to make it day. The current public use of a protected bed still allows that and can aid the owner just as much as the guest. Setting the spawn point is a secondary effect and is part of the benefit of making your own bed. I think a public-set-spawn checkbox might discourage working to create your own bed.
Perhaps a notice on protected beds indicating that the spawn point is not set would be helpful. Also, currently the spawn point can only be set at night. Is this desired, or should we allow setting the spawn point even during the day without laying down? I know other bed mods allow this action.