Baggage claim areas for domestic flights are typically in public areas. So you have a few issues to deal with.
Security may (or may not) notice your bag on the carousel after everything else has gone. You now have to spend extra time searching for security.
If there are many flights, another flight's bags may be using the same carousel by the time you get there. So your bag is still going around and around but you don't know where because your flight dropped off the sign.
Your bag is at a much higher risk of theft. If it's just sitting there when the rest of the flight is gone, a thief will think (correctly) that they can probably pick up the bag and get out of the airport before anyone notices.
The airlines will do nothing for you here. WAY too much work to single out one bag at the destination and hold it somewhere.
So which is more important to you? The caramel Caffè Marocchino in concourse B, or not having your suitcase stolen?
Note: none of the above applies to international arrivals. Arriving and departing passengers are completely separate, there are NO services of any kind between the gate and immigration, you cannot return and claim your bag later, and anyone loitering around in an obvious way will either be hustled out the door by security or put in an interview room for a while.