When you shoot 'em all, you usually don't shoot any single event at the very top level. But you do have more fun. This stuff is a game, after all. If not, find another game. ATA trap shooting and most trap guns built for ATA trap have little in common with skeet or clays or hunting or anything else.
Trap is a specialized game of specialized skills.
To get good at ATA trap, you have to train yourself to do things that will absolutely kill you in the other shotgun sports. It's a tribute to the quality of trap shooters that so many of them are so versatile in spite of this. Most ATA trap shooters set their guns up to shoot fairly high with firm cheek pressure. The premounted gun lets them tuck in nice and tight, while the predictably rising target makes a high shooting gun suitable. Unfortunately, over half of the sporting clays shots you will see are falling targets.