The OP's issue is basically: rogues don't have the best Spot check. Clerics end up being good at it, too (which seems counter-intuitive).
I don't really see this as a problem. A rogue with a high WIS will still be better than a cleric, and it's fine for there to be more than one way to skin a cat/arrive at a high check bonus. It's okay to have cleric/druid capable of spotting a trap, a mage (or a fighter not wearing armor) being pretty good at sneaking around, or, conversely, a mage or a thief capable of hitting and doing meaningful damage with a weapon (at least against certain enemy types).
Besides, there are plenty of good reasons not to have your priest out in front on trap-finding duty... doesn't seem like a big deal in practice. I'd probably declare Spot dependent either on WIS or INT and leave it at that.
I agree. This whole change to the skill system seems like trying to patch a screen door with a jackhammer: it not only causes a great deal of peripheral damage, it doesn't even address the original problem.
Issue: This new system would encourage min/maxers to train skills in their worst stats, since if my fighter has 8 int and 18 dex, training in Acrobatics is only a +1 but training in Knowledge (Arcana) gives me +6.
Issue: It's highly counterintuitive that the most effective, say, Diplomat in the game can have Cha as a dump score (as long as he took a diplomatic background).
Issue: This system would make for some weird DC effects. Like, every rogue thief in the known universe can always spot and disarm a DC 15 trap and open a DC 15 lock, but up the DC to 16 and their success rate goes from 100% to 50%. This is an artifact of the rogue's skill mastery ability, but if skill bonuses are affected by stats, at least there's some variation in these hard-and-fast DCs based on bonuses to ability scores.
Issue: The playtest rogue would STILL HAVE A -1 PERCEPTION SCORE, since he's not friggin' trained in it! And if he WAS trained in it, there wouldn't be a problem under the existing rules to begin with; he would have a minimum result of 12, way better than the cleric's minimum result of 5. His average roll would be 14.75, while the cleric's average is 14.5. If both the rogue and the cleric had the Soldier background for trained perception, then the cleric would have a range of 8-27, and the rogue would have a range of 12-22; in that case, the cleric would have a higher average result and a higher maximum result, but that's okay because he's a friggin' zen warrior. And he'd STILL get beat out by the rogue 20% of the time.
I think the easiest way to fix this would be to change the "thief" scheme to have perception as a trained skill - that is, if it really needs fixing. Personally, I'd just swap the commoner background for soldier, if I was playing the rogue. The biggest lesson I take from this whole thing is that Perception (and Stealth) are way more important in combat than any other skill available in the playtest, and it behooves a min/maxed rogue to be trained in both (since skill mastery makes training so important); I would argue that both these skills should be trained for most or all of the rogue schemes.
TLDR: The overall system is fine as it is; just make sure you choose your trained skills carefully, especially as a rogue. The devs might want to take steps to ensure that Perception and Stealth are readily available (or even automatic) as trained skills for rogues, since any rogue without them is at a big disadvantage (whereas almost every other skill in the playtest, like Folklore or Animal Handling, is much more tied to roleplaying than combat).