Had the same issue and looked at the options. Flatbeds have a higher load floor due to having both long and cross supports, typically more than 4 " higher. They also are pretty heavy ( unless aluminum, but then even more $$$) since they are built to handle heavy loads placed anywhere on the load deck. So kind of overkill if the main purpose is towing a fiver or GN trailer. Then the extra weight impacts available pin weight. Finally, there are only a few hitches designed for flatbeds.
I opted for a custom utility bed with an engineering cost adder of $200 above the stock price. Weight increase was just 350 lbs. Still have a shallow bed depth of 13 ", a tailgate that opens 180 degrees so it can't be hit and 4 storage compartments. Bed rail height is 50 " so the fiver tows level with 10 " of clearance and standing flat footed I can operate the hitch. Purchased the bed in 2003 and it is now on the second truck and will outlast my needs.