Today we have 7 recycling codes on plastics. A recent proposal would increase that to 140 codes, in an effort to make it easier to recycle 3d printed objects.
A better solution is to put something like QR codes on everything that is 3D printed (and even things that are not 3D printed), and have an online database linking codes to instructions for how to destruct that object that a 3D unprinter could follow to automatically destroy the thing. You could have a unique code per object if you wanted to, but that would be a lot of instructions for the database to store.
This is better than, say, 140 predetermined recycling categories.
This generalizes ... all that's needed is some form of tagging of objects (QR code, RFID, barcode, printed name), and some standard way of looking those IDs up online (database, web page, online form). What is linked to would be a description of the object, and one of the many links in that description would be to how to destruct that object.
If a home device is going to destruct objects automatically, the process of finding an interpreting the instructions for destruction would have to be automatable. In particular there would be standard interfaces for saying how to disassemble, dissolve, melt, burn et cetera the parts. I was just chopping up cardboard boxes by hand, which occasionally have manually-applied tape and staples ... there would be variety in how the home devices interpret the destruction instructions, too. There would be a market for new and better interpretations for chopping up boxes, and dealing with boards with nails, etc. The ability of these devices to destruct and recycle things would improve over time as the online instructions and the per-device interpretations improve.
Efficient recycling is vital to home 3D printing taking off. Without it, things that get printed have to be thrown out, or they build up as clutter. With efficient recycling, what to do with the printed object once you're done using it stops being a concern.