I'll throw in my experience and recommendation which is a little different.

First, I don't remember ever being forced to change rooms when making multiple separate reservations (assuming the room type is the same across all of the reservations though I'm sure it could happen.) It is actually in the hotel's best interest to only have to clean one room rather than 2. So they actually would prefer you to stay in the same room as well. There are some that will try to play the free upgrade game by paying for an upgrade room for the 1st night but have a base room for the 2nd night in hopes that the hotel will go ahead and leave you in that upgraded room for the duration of your stay. That can work, but not always. If someone is willing to play that game (and I admit I have tried it a few times myself), just realize that it does increase the risk of having to change rooms.

The main time I could see a hotel requiring someone with the same room type across all the reservations being asked to change rooms might be if the hotel is full. But even then they can usually find a way to keep you in that same room or at least they have for me. Though if you have a suite room or other very limited number room type and the hotel is full, I could see the possibility of being forced to change rooms. But as I mentioned, in 30+ years of travelling, if all my reservations have the same room type, I've never had to change rooms during my stay when I reserved a standard room type.

Second, my go to strategy is to make multiple single night reservations rather than one longer reservation unless there is a driver for a single reservation (i.e. staying 5 nights and can get a 5th night free award, hotel requires more than 1 night reservations, there is a price break for a longer reservation, etc.). The reason is if I need to change my check-in or out dates, it is much easier to just cancel the single night reservation rather than having to cancel a longer reservation and "hope" the points/cash rates haven't gone up.