In theory, you can remelt. Unfortunately, the practicalities mean it’s not viable. Each remelt cycle degrades the plastic itself, so you can only put 20% or so ‘old’ plastic into the mix. Combined with the game of plasticisers (to remove brittleness) and reliable forming, even commercial systems struggle, let alone home ones.

If environmental concerns are the issue. It’s best to print in uncoloured PLA filament. PLA is corn starch based, and decomposes in a bio reactor environment (it rots quickly in an industrial composter).

As for speed. They are getting impressively fast. A calibration cube takes around 20 minutes, though less than 5 minutes is possible. My machine is effectively fire and forget. They mess around while you are tuning them in, but once you have a good calibration, they now tend to hold it well. You’ll sit there watching it in fascination for the first few months, but that wears off.