Lasers are cheap, tracking for them is less so. To accurately read these grooves with sufficient resolution, you need 2 lasers (LPs are stereo), both looking at 45 degree inclination from different angles, and focused at the same point. That kind of accurate spatial + temporal sync ain’t trivial to accomplish. CDs/DVDs are much easier to implement. They don’t need similar resolution because digital, and they light their laser along the normal, only need to track 2 axes.
Even if you’ll manage to accurately focus both lasers, another problem is interference between left and right channel lasers.
Would aiming the lasers at slightly different spots and putting the channels back together in software work?
The technical problem is already solved, but the product costs $15k: https://diffuser.fm/laser-turntable/ As you see from the description, they did it with 5 lasers instead of 2.
A colleague was doing this in a decade ago, I wonder if he ever got it working.
[1] https://www.cse.huji.ac.il/~springer/DigitalNeedle/index.htm...
As they say, "significantly lower than the wavelength of visible light".