Herriot's books are unabashedly pre-modern veterinary practice, but it's also clear from his books that his practice was a forward-looking practice. You can see changes in how his practice operates and in what it did as the books go along. He talks about what the advent of antibiotics and other then-wonders of medication meant to his work. His practice when he started in the '40s was vastly changed by the time he was writing in the '60s and '70s, and this shows in his books. It's almost a theme of the books. It was probably much different again by the time of his death in 1995 (I can't find when he retired from veterinary practice, if he did).

But I can see a lot of Herriot in what you've written about your practice. Obviously not the techniques or medicines, but the love for your patients, the joy in seeing an animal healed by your hand, the heartbreak in when things don't go right, the laughter at what the animals (and owners) do, the frustrations at what the animals and owners do, etc. As you said, the people and animals haven't. And in both you and Herriot, you are dedicated to your work and making the best of what veterinary medicine has to offer as tools to make them better.