Sure, you may save a few dollars now. In the long run, pet owners will not save. As veterinary practices lose their pharmacy dispensing, service fees will rise. Practices have to cover the cost of all the doctor and staff time required for outside pharmacy dispensing/refill requests. My small practice already spends 1–2 HOURS of labor daily on outside medications, for which we receive nothing. Your physician happily prescribes through outside pharmacies, but is charging more than double a veterinary exam fee, often for a much shorter exam… generating 3–4 times the exam fees per hour seeing patients compared to a veterinarian.
As for buying vaccines on the internet, who do you trust as to what vaccines to buy, and when to give them? How do you make sure your animal is healthy before giving them? Giving a vaccine to an animal with even a minor fever is not useful, as the immune system will not respond properly to the vaccine. And where will you get support if your pet has an allergic reaction to that vaccine?
If you want your local veterinarians to be around when your pet gets sick, then support them. The little bit you save, plus the little bit each of your neighbors save, can quickly drive the local practice out of the community, leaving you with a corporate high-volume practice, or maybe no veterinarian at all.