From a security perspective, Wikipedia want all updates to be trackable, at least to an extent. This is done by either logging the user IP address and their login name (if not a guest).
A VPN means the user could be anyone, anywhere. If I were to logon to a VPN, "go rogue", and made false changes, they would be unable to block me. This is a risk a site like Wikipedia cannot take, so they block access via VPNs entirely. It is much easier to block an individuals IP on a case-by-case basis if required when they aren't on VPN.
As for identifying known VPNs, easy... a lot of these organisations publish their address ranges (or they can be found), and they can be blocked in bulk. Obviously there are exceptions, e.g. a user setting up their own VPN server.