In my experience, though I can't speak too much about commercial lenses for DSLR or even SLR camera systems, but can speak to some degree with regards to something like a payloads used for aerospace and defense applications.

Designs of aspheres are typically created via Zernike Polynomials. If you have access to an Optical Design program such as Code V, Zemax, OSLO, ASAP, HEXAGON (Raytheon), or Quadoa or equivalent one can spit out something called a SAG Table which takes in account the Zernike Polynomials and allows for much easier time when it comes time to produce either mold or the actual aspheric curved surface that's going to be machined.

Yes there is a downside to using plastic, namely chromatic aberration due to lack of index matching. Other issues are limitations on the bandwidth of transmitted light. Furthermore, most "plastics" used for cell phone lenses have historically been glass-like plastics such as PMMA (polymethylmethyl acrylate) or Zeonex. Most of these types of materials however are extremely sensitive in the UV. The plastic lenses also don't do well with wave front correction or even with just shaping light. To make matters worse, coating plastic is usually problematic as it doesn't do well with higher temperature coatings which tend to aid in not only anti-reflective, but also color correction and glare reduction, i.e. PECVD or other types of enhanced plasma coatings.

Using glass and by glass I mean a crystalline glass, perhaps something closer to a high grade fused silica or if budget permits sapphire or some type of chalcogenide, one gains better modeling control of the index of refraction (abbe number, glass melt, etc..) and also overall optical sensitivities and STOP (structural, thermal and optical) performance parameters. Something else to consider is the coefficient of thermal expansion between glass and metal can more easily be optimized. But all this comes at a cost.

The reason for plastic typically over glass is because of procurement and manufacturing cost. Plastic can have molds machined and have tolerances held rather tightly. Because of this it becomes much easier to pop out lenses. As of late holographic replication and lithographic roll to roll processing has also made making plastic optics a more cost effective option. This is a form of additive manufacturing and actually is probable where things are headed.

Manufacturing "glass optics" especially for aspherical optics are dependent upon first ensuring the substrate is pure and that the glass melts are consistent. In most cases glass must be thermal cycled, typically annealed to ensure and maintain rigidity. Rough machining is then performed essentially hogging out the material, in some cases only yielding between 60 to 70% of useable material. Finally and typically either some type of computer controlled polishing, MRF (magneto rheological finishing) or single point diamond lathing of the crystalline glass is performed. The final finishing steps are extremely costly as a combination of advanced metrology (i.e. MTF, interferometry, point-cloud analysis, non-contact surface analysis, various forms of spectroscopy) has to be performed to ensure that said advanced fabrication has either optimized surfaces for wavefront performance by either optimizing or in most cases eliminating mid-spatial frequencies in the form for micron to nanometer level peaks and valleys, all the while not changing or sacrificing the size and other physical dimensions and also preserving the most sensitive clear aperture (i.e. useable and functional area of the lens). It can be quite a time consuming process.

TLDR; Glass is better than Plastic, but is more costly to manufacture at scale, unless volume and market acceptance can drive the cost down.