I don't think your arguments are supporting your thesis. I can see an argument that slots prevent unwanted stacking bonuses because bonuses of a type are in the same slot, but that doesn't seem like it curtails unwanted synergies between bonuses of different types. If anything, having more slots available just increase the possibility of unwanted interactions.
The point of a slot system is to curtail magical synergies in a system in which having a lot of magic gear is considered normal, like 3.5, PF, and 4e; indeed, in those systems planning out your magic gear is an additional layer of character building. Magical synergies in 5e are already diminished by dint of not giving out many magic items, and only being able to utilize 3 "good" (i.e. "attuneable") ones, if you want to further curtail 5e characters maybe you could only allow one handheld magic item, one worn item, and one other item. Proto magic slots, really.