Earlier today I just booked a 5 nights stay in 5 separate nights because I want to preserve all the flexibility. I have never encounter any issue at check in to stay in same room for each consecutive night under separate reservation. Some hotels would combine all into one folio but some prefer me to do check out / check right back in (reprogram the keys). I myself prefer the clean accounting of check out / check right back in method as well. It is fairly easy to do it when going down to have breakfast. At some properties the FD actually already have one set of new keys waiting. I gave them the old keys they handed me the new keys. Done!

Never have an issue.

Usually I only book multiple nights in one reservation would be the 5 nights on pts so to be able have the cheapest night free. Occasionally when the cash rate is so low like in some countries I would book 3 nights stay as one reservation because the rares being so low I could not imagine it would go lower... However all other bookings I do one night at a time, often can save quite a bit due to dynamic pricing - it works both ways!