If precision in time keeping is the foremost goal one might as well buy a cheap quartz watch. Mechanical watches are imprecise by nature, so buying them for thousands of $$ is about something else.
Re: cone material in woofer/mids and its sonic influence, I tend to prefer paper variants. They’re just slightly more vibrant and naturally(?)/texturally warm sounding to my ears - very generally speaking. Never quite warmed to plastic cones like polypropylene, nor metal or ceramic variants, but there are exceptions, so whether it’s really more due to the overall nature of implementation of the design, I couldn’t say. For large diameter, not least high efficiency woofer/mids and sub-woofer cones (typically 12" on up) there’s no doubt in my mind: paper variants all day long.
Wrt. cone material of compression drivers, I’ve heard and owned polyamide, paper composite and metal variants, and largely I believe it comes down to implementation vs. the specific cone material used here. More important is the size of the diaphragms where I prefer them at 3," or - depending on the specific design parameters - bigger. This has to do with lowering distortion at their lower usage range and bettering overall physicality here crossing over to the woofer/mids (at an effectively lower XO point). If however a 2-way design with a large horn coupled to large woofer/mids is intended (like my own main speakers), both polyamide and paper composite diaphragms are moot - certainly at 3" on up - being they don’t extend high enough into HF-territory. Here metal variants like titanium, aluminum, magnesium and beryllium as stiffer materials are the obvious choice.
