I'm not sure why the Rick Steves website says that they only "allow" one carry-on bag. I have now been on five tours and, while most people have a smaller bag, there have been others with HUGE suitcases. The tour guide will not make this an issue. They certainly "allow" whatever people bring!
But it is important to remember that you really DO have to carry your own bag and that, because some hotels are on small streets in the older part of town, you might have to pull/carry the bag for several blocks. On the five trips I have taken, I think only two hotels did not have an elevator. I was only one floor up, so carrying my suitcase up was not a big deal. But others were assigned to rooms much higher up.
You might be surprised that, with a little planning, you can fit what you need in a 21" suitcase. I generally use this size (although I still check it on the airplane because I hate dragging it around airports and lifting it over my head). I also take a fairly large bag onto the airplane with one change of clothes, medications, electronics, etc. I launder some small items in the sink, but am not adverse to using the hotel laundry services for larger items. Some feel this is too expensive, but after paying thousands for a trip, a few more dollars for the convenience of someone else dealing with my laundry doesn't seem so extravagant.
But if you really feel you need the 25" case, do what some have suggested. Fill it up and walk a few blocks (preferably over some bumpy areas) and try carrying it up some stairs. Then see how you feel.