Back of the envelope math: cows live for about 20 years, but dairy cows are killed after about 4 years when their milk production slows. Assuming they are impregnated 4 times, that's (5 cows * 20 years per cow) / (4 years) = 25 times as costly. And this 25 times as costly milk has to compete with the 1 times as costly milk in a market that's already so competative that milk is sold below cost with government subsidies. It's impossible for practical purposes.
If you're comparing today's market, practices, and subsidies (which are all just measurements of the same signal) to a fictional world where we didn't want to kill any calfs, but using today's subsidies and prices, then I think that's not a fair comparison.
If god appeared and said that the Hindus were right all along and cows are sacred and milk is their gift to us - we'd do it just fine.
This is assuming that people would eat calves if they weren't killed so that we can take their milk.