I thought there were TT's using Hall-effect sensors that did essentially that (analog PLL). I know I piddled with such a circuit ages ago just to see what I could do with it. And of course a number of direct-drive TT's used PLLs for speed control. I would not use the cartridge as the sensor, however, too much else going on and the signal would be hard to pull from the music on the LP. I am not sure a software approach would do much better than an old-fashioned analog design, however; we can get femtosecond precision from a PLL used for radar, EW/ELINT, or the high-speed serial data links in your computer (PCIe, SAS/SATA). I am not sure why it would get closer than a PLL, seems like pretty much the same function to me.
One could argue a massive platter would work against the PLL circuit since you'd need a lot of torque and excellent control loop damping to adjust and maintain the platter's rotation. Back to the endless debates about smaller/lighter/tightly controlled vs. larger/heavier/lightly controlled if at all, just let inertia control speed variations. Another hot topic -- there was a lot of attention focused on making platters (spindles, bearings, etc.) that were homogeneous throughout and perfectly manufactured so the platter (etc.) did not induce its own speed variations. Then all the focus on motors and drive systems (direct, belt, idler, etc.)
Another can of worms, let's all go fishing!