Walrus- Much of the answer to your question involves tradition. Some of us remember when plastic shells first appeared on the market. All we had to shoot before that time was paper shells. Paper shells, especially Federal paper shells had their own pleasant smell after firring. That smell was due to the wax used in production of the hull. Both the smell of burning leaves in the Fall and the smell of paper hulls reminds us of the time when we were very young, and we like that.
On performance, I have shot many patterns with Federal paper hulls, and I think I can show a very slight pattern improvement with these hulls. I openly admit that I want to see a pattern improvement with these hulls and I could be shading the actual results with the results I want to see.
On the recoil reduction claims based on the compression of the paper base wad in paper hulls, I am doubtful. In theory, there would be some recoil reduction but it would be much to small to notice. Much more reduction could be gained by removing one lead pellet form the hull before crimping it.
There is a down side to loading Federal paper hulls on many reloaders. The hulls are hard to find and we try to load them more than two times. They will develop small pin holes just above the brass rim. Then in a press you can find the brass rim on the index pad and the rest of the loaded shell stuck up in a die. Somewhere I still have the tool I made to extract a loaded hull minus the brass rim form a die.
Federal Paper 3 dram (heavy) 7 1/2's were a favorite of "money" games shooters in the 1970's and 1980's and many still use them. Federal Paper 2 3/4 dram (light) 9’s were a favorite of still board target shooters for small dense patterns.
The discontinued Federal 12C1 two piece wad was a favorite wad in new and reloaded shells.
For reloading, the Federal Paper hull with its straight sides had a lot of room for heavy charges of Alliant Blue Dot, IMR 4756 and other slow burning powders.
Today, IMO, the Remington Nitro 27 is the top choice for call birds by games shooters. In games, when you get down to the last few shooters, Federal Paper reloads come out of a back pocket and into the chamber of a Model 12.
The first Trap loads I bought, back before Viet Nam, were Federal Papers in the Champion packaging. I still regard it as the most beautiful shot shell packaging of all time. I bought 3 dram 8’s for dove hunting and they would really reach out.