For the intrinsic parameters of the webcam, that is a property of the hardware and not your room, yes? If so, it seems possible to crowdsourced that information to build a database. Then for most users, it's just a matter of entering your product model rather than taking 50 checkerboard photos.
It's still not convenient, but it's a much smaller hurdle to overcome.
Agreed. My first thought was - what percentage of the target market could you serve with coding to specs for MacBooks, which have deterministic hardware.
Or if the tuning parameters exist with some range, use a traversal algorithm to find them, similar to an eye exam: “A or B? [change parameter]. A or B? [change parameter]. Repeat”
It's still not convenient, but it's a much smaller hurdle to overcome.