I'm curious to hear from people who have had more experience with this on other cruise lines, but I don't really want
DCL to do this. We had this on Celebrity and I didn't enjoy it as much as I thought I would. We had different servers every time and it was hit or miss. Although we never had to wait more than a couple minutes, but I was always nervous I would have to (which I don't have to worry about on DCL). Overall it was okay, just dinner wasn't nearly the special occasion it is on DCL - which is okay sometimes, but sometimes not.
Then we were on NCL and the couple times we tried to eat "anytime" where we wanted there was a wait so we didn't bother. The ship was super busy and crowded and a lot of people waiting to get into restaurants. I hate waiting around on a vacation! Fortunately we were staying in the Haven and we just ended up eating in the Haven restaurant or specialty restaurants (with reservations) every night.
Even when my kids were little (4 and 7) we had late dining with no problem. But we stay up later on vacation and sleep in later; and these days we eat around 7:30 normally, so 8:15 on vacation is not a big stretch. But no medical issues like the OP of course...