You forgot about polymer shortening. During the first synthesis process from petroleum to the usual type of plastic, long polymer bonds are formed which give the plastic its malleable-yet-durable characteristics. During shredding to get the plastic into a more feedable shape (as in feedable through a hopper into an extruder to be melted) those polymers are shortened. This polymer shortening ends up leading to a more brittle plastic, and because of this new plastic beads are added to rejuvinate.
Because of this, recycling plastic inherently requires new plastic in its process, and old plastic is only recyclable for a few cycles until its essentially garbage being mixed into the process.
We are essentially just pushing out the inevitable, which will be that we'll need to dispose of massive amounts of plastic waste that is unusable after a few cycles. I imagine we'll eventually just have to compress this waste into blocks and bury those blocks deep underground like nuclear waste.