Who cares where the savings comes from? If someone needs people to ride with and big rings with fancy jumps and doesn't have time due to a heavy work schedule to actually take care of a farm, then the cost savings doesn't matter - it's not for them. Heck, there are more than a few folks who go back to boarding during the Winter for the sake of some ameneties. But for many people, paying for the number of amenities are some barns is soooo not worth it. Some don't want to pay for a heated barn and hot water in the barn and someone on call all the time to put on and remove blankets on a moment's notice, or have part of board fees go to keeping the grounds in pristine shape when they have nothing to do with how the horse is kept.
If moving your horses home includes a drastic change in the standard and complexity of horse care and a significant reduction in horse/barn amenities, yes, obviously you are going to save money, just as if you moved your horse from stall board at a fancy facility to pasture board at a more simple place. The savings is not in having your horses at home, it is in the simplification of their care wherever it is.
Of course. It's one thing to shell out some money every month for someone else to do all the dirty work, it's another to actually do it yourself. If you (in general) want a pristine barn with all the niceties of a nice boarding barn, then you're going to have to work to keep it up.
Interestingly, I have had several fairly particular clients over the years who have ended up buying their own horse properties and moving their horses home and in each case their standards relaxed dramatically. It takes a lot of work to keep stalls clean, buckets fresh, blankets changed, fences fixed, arena groomed, aisle swept, etc, and when people realize exactly how much work, they often decide to drastically simplify things.