Pains with the current systems: physical document (can be lost, stolen, forgotten, etc.), harder to renew and receive when living abroad, needs to be renewed every X years (and some countries require more paperwork than others)
>> Would it make sense to have passports issued by an entity that is not a country?
Not really. What would it even mean?
If I have a digitally signed document that says "FIRST_NAME LAST_NAME is a citizen of the Internet" or "FIRST_NAME LAST_NAME is a certified member of Blockchain Buddies" would it be officially recognized by other governments?
Passports are legal documents which show that a person belongs to a certain nation and that that nation "has their back" or at a minimum where to send the person if you want to deport them.
>> How about virtual passports? Blockchain?
Nations could issue fully digital passports or identity certificates, but it does not need blockchain-based technology to work. Existing cryptography tech like digitally-signed certificates and public key cryptography are sufficient.