CW: how the dairy/meat industry works.

It's basically the same. The driving factor of mass death in the dairy industry is that to make cows produce milk they've gotta get pregnant and calf, so you end up with a bunch of cows that are too old to produce enough milk for market and a big of calves that won't produce milk, ever.

In the West, those "extra", "non-productive" animals get killed (the dairy industry is the meat industry). In India, this is still often the case as not everyone is veg and not everyone who's non-veg avoids beef. But there are enough people that refuse beef for there to be an impetus to follow a "traditional" alternative: you kick the animal out of the dairy for it to fend for itself. In reality, they tend to just starve to death over a long period of time.

For there to be dairy without a culling there would need to be like 30 pet cows for every 1 dairy cow. Assuming the cost of raising the cow is what people pay for, that would mean milk costing 10X more.

It depends. India does have some factory farms, mainly for beef. But many dairy cattle are kept by small farmers for whom the milk and meat are a supplement to whatever plants they grow. And these farmers usually belong to dairy co-operative societies like Amul, which do quality control and ensure that the animals are not abused too much. Also some Indian states ban or heavily restrict the slaughter of cattle (although in practise this just leads to them being abandoned or disappearing into the black market).