Investors can only invest in scalable, replicable businesses. Veterinary practices are intensely personal, often specialize in different species and breeds, and can develop unique experimental treatments. The cost of labor is ridiculously cheap (people become Vet Tech's for love, not money), and buildings need not be in commercial centers, so capital costs are minimal.
Honestly, veterinarians are really in the best possible profession for maintaining independent practices. If they can't resist investor takeover, who can?