Cats can do it because of their width and speed. Some traditional boats with lug or sprit rigs are boomless. My Dory has a sprit rig that sailed boomless for many years. I added a boom for easier sheeting and better down wind shape. A great advantage of small boats (the dory is <19') is the ability to cheaply experiment with the rig.
The boom transmits much of the drive to the mast. Without it a 30' sloop would need mainsheet winches. It would also change the balance.