You can absolutely have signature required to a PO Box if using UPSP Priority Mail. I have a PO Box and when I get a package, they leave a note in my box that I take to the counter. The counter person gets my package from the back and I sign for it.
Some people may not know this and that's why they're hesitant to ship to a PO Box. (?) I don't know about APO/FPO boxes.
Also if the shipper uses FedEx, UPS or DHL, they do not deliver to PO Boxes - they need a physical address instead.
Hope this helps!