I'm no where close to that point but I had a theory someone may be able to confirm. People tend to buy the cheaper packs to fill up the sticker book, these guarantee a rare but that is all. Add to this the fact that most accessories have multiple levels that can only be found in succession. (Normal -> Silver -> Gold -> Diamond -> Gem?)
Anyway, I had a theory that the reason for the stranglehold is not bad programming or malice, (Which is odd, that is usually my go to with EA) instead I think it is due to Super Rares. See, people get the cheap packs and only sometimes get Super Rares, this leaves a massive backlog when you reach a certain point in collecting. (when you run out of commons, uncommons and rares) So, with only one Super Rare guaranteed and only in 35K+ packs it seems like a slow leak of collectables past a certain point. When in reality it is just the many Super Rares slowly being added one at a time and only when the previous level has already been collected.
I'm just trying to be optimistic. (Which is hard since each aspect of the game is rapidly becoming frustrating.) But, someone who is at the point of slow collecting would need to look into it. (It'll likely be months, or at least until the next discount days before I can check myself.)