"Dear EarthTalk: Why can’t plastics of all types, instead of being initially sorted, simply be melted together to be separated later?"Overlooking the simple issue that each individual polymer has separate melting/softening temperatures and just shooting for the highest temperature needed would degrade the lower melting materials, there are thermodynamic issues as well involved that challenge all polymer scientists and engineers that are looking to make a compatible blend between two polymers (never mind attempting to blend all 6 different versions of purified streams available after sorting by hand).
Compatible blends of polymers are very much an exception and not the rule. Small differences in polymers can have a tremendous impact on solubility. The most extreme example that I'm aware of is deuterated polymers phase separating from their non-deuterated equivalents. The only possibility more extreme would be a homopolymer separating from itself - and even that isn't that remote of a possibility at times (such as in field-flow fractionation).
Polymer compatibility is challenging and it is all because of the high molecular weight of the materials involved. Little help is provided from entropy (the number of molecules per unit volume is so much smaller than for a low molecular weight material) and so much is therefore requested from the enthalpic interactions which occur at every repeat unit. If the interactions aren't right, you will not have a soluble mixture since there are so many of them.
It would be great if these constraints didn't exist and all plastics could be thrown into a big gemisch, but that won't happy anytime soon and probably not ever.