Identity theft in Europe is extremely rare. It is possible to do something in your name, sure, but it does not happen nowhere near as often and damage is limited compared to ssn system.

Not gonna happen, banks for now will rather swallow the relatively low loses due to fraud.

In USA you sign a piece of paper (pre-approved loan), or login online and the loan money is deposited in your account within a few days. All automated. So far it works out for them, if fraud loses increase, the banks, not us, will choose the next method. And Congress will approve it within weeks.

It should not be a passport number or driver's license number. It should be the original, physical passport or driver's license that you present in person. The physical object is much harder to steal or copy, and can be revoked.

You should not be able to open credit lines or accounts with a business without appearing at least once in person first.

The national ID also has an embedded smart card usable for authentication but for some reason using that has never took off.

Video is just another form of photo copy, so how would that work?

All in all this process makes it much much harder to steal an identity. Also, once you report your ID card stolen, its serial number will be blacklisted preventing it from being used. Add to this that there is a snail mail address on your cards which will typically be used to send login information such as passwords and PINS

Also, please don't use terms like "steal an identity", that is how banks frame things in order to make it appear that they are not responsible. Banks don't employ reliable authentication, thus they get defrauded by imposters--nothing is ever stolen from those who the importers pretend to be, it's only between the bank and the imposter, noone else is a party to that fraudulent transaction.

For now, it remains somewhat secure in practice and will hopefully bye augmented by use of cryptography already available in many IDs (though, as other comments note, not widely used in some countries)