Thanks Andrew! Yes, the question you raised is the most critical one in the plastics system. Plastics are assigned Resin Codes from 1-7 (the number within the 3 triangular arrows that you see on all plastic materials). The arrows have nothing to do with recycling and the numbers only indicate the chemicals used in the plastic.
PET is classified as a Code 1 material whereas polypropylene (PP) is assigned Code 5. To the best of my knowledge, in the current system only Code 1 and Code 2 materials are "down-cycled" (not recycled) into Code 3-7 materials.
The used Code 3-7 materials are either incinerated or sent to a landfill or worse, dumped in the oceans.
So, to answer your questions: "Could they only be recycled into low grade, single use, polymers?" Only the PET bottles will get recycled ("down-cycled" actually), into low grade single use plastics. Materials have to have the same Code to be treated together so the bottles (Code 1) and bottle-caps (Code 5) cannot be treated together. Even when materials with the same Code are treated together, internal variations (due to chemicals to change the color, texture etc. of the bottle) can create problems.
"Or could they be recycled into high grade multi-use PET and polypropylene polymers, basically becoming the same materials they were before but in raw form?" No plastic ever gets recycled into its original form. After the first down-cycle, Code 1 and 2 materials become Code 3/4/5/6/7 materials.
The scope of this challenge is mainly to address these Code 3-7 materials as they have no utility at all after they are used. The main problem is that differently coded materials cannot be treated together due to their chemical differences. However all plastics share the property of low thermal conductivity irrespective of their Resin Code numbers. Hence it is possible to shred and reuse them as insulating material (especially in non-temperature critical situations -- i.e. where small temperature variations are not catastrophic -- such as housing and office spaces). This is nothing new and has been successfully used in low temperature locations such as Kathmandu. Not only does this get plastic out of the system and avoid energy consumption and toxic emissions of plastic incineration, it also reduces heating costs.