In contrast, I can't say I've ever heard of seats in cars having this problem. Is it because plane seats are highly optimised for weight?
Suppose your plane seat hasn’t locked. You taxi around to the runway (slow and always level), then you begin the takeoff run. Already, you have some acceleration pulling back. Then you gently pull back the yoke to rotate. Now, suddenly your seat slides back. You hold onto the yoke, stall, and die. Or you let go off the yoke, and now the plane is unpiloted in the crucial take-off phase. And, note, stopping is not an option at this point.
That’s why vigorously thrashing around in your seat is part of the before-takeoff checklist (“Seat - LOCKED”).
Also, what about adjusting the steering wheel while driving? Sounds like a similar threat.
And because it would be less likely fatal in the car, so you'd be less likely to hear of it happening.
(Less likely fatal because car collisions are less fatal due to e.g. airbags, and less likely to impact terrain since it only takes a second to undo your car seatbelt, and because there's no pitch control to have messed up.)
"Serious" is still not the same as "fatal", even if your car hits something. If your plane stalls and falls hundreds of feet, my understanding is that the fatality rate is going to approximate 100%.