Some sellers have not found where they will move to or do not want to cram closing and moving into one day so post closing possession gives them a buffer. Post closing possession does need to be outlined in the contract or added later via attorney review. The buyer and seller do have to agree on these terms. Sometimes my seller client's want to add possession for peace of mind and in many instances end up not needing it or just needing a couple days.
Regardless of common practice, I would agree that it seems most buyers want to take possession at closing. I could see how possession could potentially jeopardize a sale for a buyer, so I would do everything I could to work with them.
That wasn't the way it ever was, either. Yours might have been a specially negotiated situation, but the new buyers plan to move in when they own it, not a few months down the line.
All the best,
The most common thing is to vacate by closing. Sometimes if you are selling and buying, you can ask for a few days to close your sale and then close your purchase and move. It just comes down to what you negotiate. When your house is sold and closed, it's no longer your house so anything past that depends on what the buyer agrees to up front.
There is a provision built right into our local contract to handle it.