Hardly anyone is paper anymore.

There's a lot of vet management software, but really only two that matter - Cornerstone and IDEXX.

All the vet schools use one or the other, and so do the vast majority of large vet clinics and corporations where young vets get their first jobs. If they ever start their own practice, they've already gotten use to Cornerstone/IDEXX, so there's no reason for them to switch.

There's little demand from clients to see their records online or transfer their records electronically. Sorry, HN crowd, but that's just the way it is with non-techies. The practices that do offer it use a number of third party integration services. However, the demand is so low, those companies hardly make any money because they can't charge very much.