This is the general idea. In North America, the checkout procedure is a bit different than Europe, Asia, and Australia/NZ. Normally here the hotel will simply slip the bill under your door during the last night of your stay. The hotel will do a reprint in case there are incidental charges prior to checking out. Otherwise, the hotel will charge the card on file from check-in. This can happen when you visit reception upon leaving but not always. Sometimes the hotel processes the charge later in the day. As I only have USD cards, I can't claim any DCC issues with the major hotel chains in the US. I'm not saying it doesn't exist, but I haven't read any reports or complaints.

In other parts of the world, one tends to settle the hotel charges with a single card present transaction upon checking out. For these situations, I will use an AmEx checking in for the preauth. In the case of a non-Marriott or non-SPG property, I will switch the AmEx to either a cobranded card or something like the Chase Sapphire Reserve for an independent hotel upon checking out. This avoids the property from automatically charging the preauth card for the amount of the hotel room and accumulated incidental charges.