YESS this is such a good idea!! Even with paying for a sitter every week, it can even be a pain/hard to remember to come back exactly 7 days afterward to renew the sitter so your pet doesn't run away... although the new daycare update is real nice and might help make keeping pets without daily interaction easier, something like this would STILL be extremely beneficial! :O
EDIT: it turns out, putting an active pet into the nursery costs 2k credits, so the daycare definitely Won't act as a good substitute for the sitter alternative, considering the price you'd have to pay every time you would want to take your pet out, interact with it, and put it back in... I absolutely stand by your suggestion of a sitter subscription, i really love that!! And I'm glad I'm not the only one daunted by the amount of interaction a pet needs in order for it to not run away LOL