I have kept Jersey house cows for eight years now. Our latest addition is a crossbred daughter of my original matriarch Jersey. The new entrant is a Red Devon cross Jersey.
First of all, I have milked three of my Jerseys and the one crossbreed, and if you blindfolded me and gave me some of their milk to drink I would be able to tell you which cow it came from, and whether she was eating predominantly grass at the moment or not.
My first cow, Hillie, is an amazing animal with incredibly rich milk. Picture of her midsummer produce attached. Not so much "gold top" as "white bottom"!

And yes, the cream, butter and cheese are also very rich. Personally I adore butter made from Hillie's cream, but it does very quickly get that sharp taste unless you are very thorough about washing it until the washing water is sparkling clean - and then pat it throughly to get any remaining water out. I don't like my butter salted, so that makes it harder to drive the water out. Also, we let the cream rise and then skim, rather than using a separator, so the cream has "matured" for a day or three by the time we churn it.
In Cumbria, I would make 1/2 a jam jar of yesterday's cream into butter every day, and we would eat that in 24 hours. It was never rancid, always fantastic
I haven't yet had a go at making a cultured butter - Christine Paige at Smiling Tree Farm (pasture-fed Jerseys in Shropshire) recommends this, and I think it could address the sharp taste thing.
Hillie's milk has successfully reared lambs; many, many calves; augmented pigs' diets and those of puppies... I always meant to make a collage of what her first lactation gave us. I think it was 5 calves, 10 or more lambs, 2 pigs, two hounds, and of course ourselves.
I have never ever had a calf scour on Hillie's milk. She has reared her own calf every lactation; after about one month old we usually separate the calf overnight, but they are together all day with the calf or calves drinking at will. Until being in a community, Hillie always had more milk than we and her calf needed, so I would bring in extra calves. Most lactations she would have her own calf for 5 months, a same-age companion for it for 4 months, then another pair of calves brought in at a month old and fed for 3 months, and occasionally another calf or once another pair for a couple of months or more, depending on when her next calf was due.
I would always take care that the calves couldn't gorge when going back onto her in the morning after milking, and when introducing new calves I would manage every feed for the first few days while they got used to her milk and that they would have plenty of it ad lib, so didn't need to gorge.
i have written about using her milk for lambs on the forum. Basically I never had a problem with scouring; I found they needed about a litre and a half a day at full capacity; I did find that lambs would scour - and two died before I sussed how to handle this - if I put them back on a ewe after they'd been on Hillie's milk for more than a few days. After I realised, I would give any lambs that were suitable for adoption half-and-half Hillie milk and ewe milk replacer, and they seemed to be able to switch back to a ewe no problem from that regime. Once they were clearly not going to be adopted, I could put them on 100% Hillie milk.
We believe that Hillie is A2, in that several people who thought they had a cows' milk intolerance or allergy have found that Hillie's milk has no adverse effects on them. I have wondered whether the ease with which all species seem to take to Hillie's milk is connected to her being A2

However, I've also realised that she was always on largely unimproved Cumbrian upland when I was doing all those things. (Down here the pigs get whey from cheese-making and any unused cream, but we don't get a lot of pet lambs and haven't had any hound pups.) Hillie's summer milk was about 1/3 cream up in Cumbria.
Hillie is wonderful but she is a high-performance animal and she takes a heck of a lot more looking after - and food! - than a suckler cow!
She is not hardy, and really needs a dry bed in winter at least. One of her purebred daughters was a much hardier animal, but she didn't take to being milked so was used to rear calves. One of the other daughters was the opposite; loved being milked, was an utter sweetheart in the parlour, but wouldn't take to another calf, would only rear her own.
I have not had a problem with milk fever, but I don't push them and I take care that they have rock salt all the time, and extra minerals in the couple of months before calving. I give some feed for the month before calving too, which is grass pellets now that we have gone pasture-fed.
Ex-BH used to feed a dry cow half a small bale of hay a day, or reckon on 15-22 cows eating a big round bale of haylage in 24-36 hours. Hillie eats at least twice that, plus a bit of hard feed (now grass pellets) in the parlour. I have found that grass makes milk and flesh, hay makes flesh but not much milk; good meadow haylage makes milk and a bit of flesh. Rye haylage makes wet poop and goes through so fast I'm not convinced it has any nutritional value at all! lol
She has literally a handful of pellets to get her head in her bowl while I tie her up, and only has more pellets than that in the month before calving (when she's dry, of course) and if she seems to need more input early on in her lactation.
It took me a while to catch her to the AI after her first calf (which was a natural service.) Since realising just how sensitive to change they are, we've had no problem with her - but I don't serve her if I know there is a big change in the next six weeks

There have been three occasions on which she has skipped a year or had an eighteen month lactation. She milks through, gives a bit less the second year but still plenty for us, and I've always given her a longer dry period if she's had a long lactation.
They say that older Jerseys are prone to mastitis and also to Johnnes. Hillie has had mastitis three times since I moved to Cornwall but I am sure that is mostly down to us not managing her perfectly. (We have made some changes, so fingers crossed for the next lactation

) Hillie's poo is always wetter than Flare's, and Hillie is not an animal that carries a lot of flesh. She can get really quite thin at times when there is not a great deal of grass, but she is able to replenish her modest covering when the grass comes back. One year here we had a long drought, and she had a calf on her, so I stopped milking her until the weather changed and the grass came back.
Flare, the crossbred daughter, is much more of a suckler type physically; she is hardy and a "good doer" - and gives way less milk than Hillie. We milked her to train her but did not separate the calf at all, and basically have only been getting enough milk to do anything with since the calf went. (He was an Angus cross, made 244kgs deadweight at 10 months old, off grass and milk only. Spectacular

) Flare's milk is crisp, white and has a "clean" taste compared to Hillie's. It has a reasonable layer of cream; the cream is thinner and whiter than Hillie's. (But you would never call her milk or cream "watery".) I think Flare's milk will make awesome soft cheeses, and a really fresh-tasting yoghurt.
I adore Hillie and wouldn't change her for the world, as you can probably tell! If you want to multiple suckle, I think the right Jersey will pay for herself many, many times over. But they do have very distinct personalities, and not all will take to multiple suckling.