In addition to what OneShot mentioned, there would be the issue that limiting someone to one triggering action let's you do all sorts of undesired shenanigans.
Consider the following situation: A magus's lab has been protected with a whole bunch of enchanted items that can be triggered accidentally by an intruder, and a grog with a ring that improves his Soak for Diameter an unlimited number of times per day wants to steal an item from the lab. So the grog activates his ring each round while moving through the lab to prevent activating any item in the lab accidentally.
Or this one: A trained group of grogs each have a suit of armor that deflects an animal/beast if it strikes the armor like The Wizard's Parry. They face a hydra that functions somewhat like The Blessing of Starkad. The hydra attacks with its bites, hitting the group for one apiece. One of the grog's suits of armor functions, while the rest fail because the hydra has already triggered one effect.
But "use one effect from one item each round" remains really messy itself. I really don't know what the right way about this is. The intention is that you cannot do a whole bunch of different triggering activities to benefit yourself in one round. But you should be able to trigger a bunch of things with one activity (e.g. Multiple Casting with ReVi, effects with linked triggers) and trigger a bunch of different negative things (e.g. the grog in the lab above, the hydra above).