The plastic used in ICs is typically an epoxy resin, as opposed to a thermoplastic. A thermoplastic will melt and solidify with temperature, whereas as an epoxy will set through a chemical reaction and won't melt. They are also mechanically rigid, excellent electrical insulators, anhydrous and chemically inert, all of which are anywhere between highly desirable and required features for devices used in production of electronics. Now, the problem is that most or all bioplastics are thermoplastics. This is great for 3D printing, but not so great for chips.
For example, you'd be hard pressed to find a bioplastic which has a high enough melting point to tolerate soldering which will reach a minimum of 200 ºC for reflow soldering, more for other methods, including manual soldering with a soldering iron.
Other problems that I would predict: Poor bonding to the die and bond wires, which will let moisture creep in and destroy the die. Poor heat conductivity. Might melt or otherwise react with the die and destroy it. Might melt from the heat generated by the die and become a good enough conductor on the microscopic level to create faults. Might have unsuitable dielectric properties and leak high frequency signals between different nearby traces on the die.
But the kicker is that the tiny amount of plastic used in the production of a chip i probably the least of the problems environmentally speaking. A typical consumer product will contain in the order of hundreds to thousands amount the plastic used in the chip in the case. Producing the die requires the use of various nasty chemicals, for example trichloroethylene which is used for washing the die. Any serious manufacturer will keep their trichloroethylene in a closed loop system, but to mention a famous example, there was a leak in the facilities of MOS Technology, Commodore's chip plant, which forced the city to build a water pipeline from a nearby city because the groundwater was ruined. How do the less scrupulous Chinese IC manufacturers dispose of their chemicals I wonder?
But my bottom line, and this may perhaps sound a bit hostile, is that you can't just slap a buzzword onto an industrial process. If something hasn't been tried it's often because it's not a good idea.