> How else should verification be handled?

Many European countries have secure electronic identifications that are trusted by the government, banks etc.

Linkedin could easily use this to verify the identities.

Example of services where you can verify the identity with 35 different providers using a single API:

https://www.signicat.com/products/identity-proofing/eid-hub or https://www.scrive.com/products/eid-hub

I doubt it would take more than a sprint to integrate with this or other services.