Okay........this may fall under "having your own schedule," but, the only real issue that has sort of had us stressing a bit is when the tour bus needs to leave at X time, and five minutes before that time, spouse needs to do his "morning business." We were a minute or two late one time on a RS tour because of that...and then hard to explain "hubby needed to ________"
Another time, on a shore excursion from a small ship in Quebec, my husband really needed to find a bathroom because he had too much coffee that morning (lesson learned in that). The leader of that group walking tour was not having it, just telling him to wait. We excused ourselves from the tour, and I dashed up to the large hotel there (cannot recall the name right now) and FOUND a bathroom for him. The tour leader was aghast that we left (but she was not being realistic with his need)...luckily the group had walked from the ship, and we knew we would find our way back without problem.
Another time on a group shore excursion off another much nicer high-end small ship brand, an elderly gentleman really needed a bathroom while visiting the area where the shops are in Mykonos....the tour leader kept telling him they could not use shop bathrooms and to "just wait." The man asked about 5 times, really needing "to go." I think had that been my husband, we would have handed a shopkeeper $20 and begged.
So, that is very personal stuff, but it can happen to anyone.....be it a young lady needing a "that time of month" personal time, or an older guy with timing not perfect for the tour bus meet-up.
Otherwise, we have always enjoyed our group tours.....and great guides always advise of bathroom breaks, etc.
Granted on the RS Tours, there is a bathroom on the bus, but I will never forget how one dear young lady was "sort of group shamed" about using the bathroom, after the RS guide for the "Heart of Italy" (or whatever it was called) tour had pretty much begged people to NOT use the bus restroom so the driver would not have to have the tank emptied for one or two uses........so there is that, too. The shaming was done with some humor, but still!!
I agree with the advice above that if traveling as a party of one, get a solo room. After a long day, the wrong roommate could be grating. Heck, spouses can be too.....LOL, but love over-arches.