As someone who has been very deep down this rabbit hole and hacked together multiple path and velocity trackers over the years (specifically for olympic weightlifting), there is no extra information that tracking bar path will give you that simply looking at the video won't, and often just adds more clutter. You don't need to graph bar path to see that the bar is looping too far forward after hip contact in the snatch.

Velocity on the other hand is a great metric to track and is used as a proxy for RPE. Mike Tuchscherer was the first one to systematize it for powerlifting a while back, if you've been lifting for 20 years you're probably aware of the name.

Thanks! I think for "canonical" lifts (squat, deadlift, row, to some extent military press) the vertical bar path is mathematically optimal, and for all kinds of lateral or sagittal movements you do more work with weak stabilizing muscles and load joints laterally too. Is it productive work that strengthens your core? Possibly, but it's hard to quantify. It it something that can lead to injury? Absolutely yes.

For more complicated lifts like bench press (J-shaped) or snatch (S-shaped), for example, I would rather set a "golden sample" path with a coach and compare to that.

It's unlikely to be the sole metric, especially given the inverse kinematics of different body types (long/short femur, etc), but together with bar speed, over time, it can provide a lot of good feedback.

Not OP but velocity is typically what these devices are used for. Its a great measure of between-set intensity.