This article has the best account of why its use was/is so widespread. Here are some select lines from the article:
The introduction of hybrid cows in India coincided with global trends of the chemicalization of agriculture, medicine, and veterinary science.
In the shadow of antibiotics, diclofenac, a common painkiller also for human use, has become a “blockbuster drug” in more-than-human medicine. High-yielding cows undergo relentless cycles of pregnancy by artificial insemination, birth, and lactation. In India, diclofenac was the drug of choice to treat the many pains of high-performance cows, among them mastitis, a painful inflammation of the udder.
Diclofenac is a cheap, nonsteroidal anti-inflammatory drug (NSAID) and thus within the same class of pharmaceuticals as aspirin (ASS) or ibuprofen.
Diclofenac has been sold since 1973 under the brand name Voltaren as an over-the-counter remedy for arthritis pain in humans and domestic animals. With the end of patent protection, it has become one of the most widely used NSAIDs across the world, and its generics are available in India under a variety of brands.
Human and other mammalian bodies metabolize diclofenac and excrete it via the kidneys and the renal system. Healthy mammalian kidneys can deal with the drug reasonably well. To birds, however, diclofenac is a deadly toxin. Birds who ingest diclofenac die of severe renal failure as the effect of kidney necrosis.
Based on emerging evidence of avian kidney toxicity, scientific and political pressure led to the eventual ban of diclofenac for veterinary use in India in 2006. However, many veterinarians consider diclofenac so important for the care of milk cows that they continue to use the drug illegally by misappropriating drugs designated for human use only. Pharmaceutical companies played along by labeling the liquid 30 ml vials, popular among veterinarians injecting the drug, as multi-dosage preparations for human usage