I'm struggling to understand why you don't characterize this mechanic as "counting successes". Yes, the dice are somewhat more complicated than coins (though right off the top of my head, I'm not sure how radically different the expected number of successes would be if they were coins), and yes you are actually adding up the number of successes that modify your base degree of success based on what you are testing, but it's still very much a dice pool mechanic that involves counting the number of successes and comparing it to a target number.
You're not counting successes. The dice are +1, 0, or -1; you're generating a sum, in a range of -4 to +4. Gets added to your score in the relevant ability and compared against the difficulty of the task. I'm not the biggest fan of FATE, but the dice are not any part of my problems with it.