It's a situation that basically has to make sense to the person doing it. I have done both, for many years. I personally prefer the nurse cow routine. Takes a bit to get them established sometimes, but once they are, then it is a next to no labor deal.
Here a normal dairy figures one bag of milk replacer to get a calf to 6-9 weeks weaning. But the added cost of good milk replacer, and grain, and labor gets the calf to about $250-300 just to the 8-12 week age. Then you are talking a fair amount of grain for the protein and all to grow the calf. Most dairy farmers figure that it costs between $1500 - $2000 to get a heifer into the milking herd. Beef will cost a bit less, but if a person were to figure in everything, a decent average beef heifer ready to calve you will have at least $1500 in her.
For me, and I did the figures several years back; if I had a nurse cow that would raise 3 calves, with the added grain I fed her to keep her production up for the first 3-4 months, it would cost me about $1000-$1200 for her for the year; grain, pasture, hay, and my extra labor for the first couple of months. But then I figure she is giving me back about $1500 in calf sales, or more. So I figured that 2 calves paid for her and the third was profit. Since then, milk replacer has gotten higher $75 a bag verses $60. Grain is a bit more and hay runs about the same on good years. Still, a calf will naturally just grow better on a cow by getting milk when it wants, as much as it wants. I think everyone can mostly agree with a beef calf does better on his momma than on a bottle
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If you have the cows and milk them and bottle feed the milk you can raise a couple more, and supplement with grain like Aaron's neighbor probably does and still come out ahead. There's a little more labor, a little more feed costs, but he is getting more calves for it than if he just put 2 or 3 on each cow. He is also probably getting milk for himself for the house so there is that benefit. That is why I will often bring my cows into the barn even when the calves are established, and maybe keep the calves off one of the cows for 12 hours and milk her for the house too. I also have one cow that is only a 3 teat girl, that will come in and I can milk a gal or so once a day and she usually has 1 or 2 calves on her too, without having to keep the calves off for the 12 hours. So she is usually the designated "milk cow" plus the 2 calves she is feeding. Even if she is only feeding one calf, that is all we require from a beef cow so she is basically paying her way if not making me much extra. Last year she had her purebred jersey heifer on her and I milked her 2-3 times a week for the house and I said she paid for herself. The calf is real nice, and I got all the milk I wanted and when I got to the point of her getting up in days of milk, I quit grain feeding her, quit milking her and then I dried her off when I took the calf away and weaned it.
There is no perfect way to do it. To each his own, but I do feel it is cheaper and better for the calves to have nurse cows, or milk cows that you feed REAL MILK to the calves you are bottle raising. And the milk cow can reproduce herself which the bag of milk replacer sure can't do.