It's literally never occurred to me before.
There were plenty of times when a scene would be described as "We see the family on a normal Saturday night. Dad is sat in front of the TV, mum is sat at the table, doing a jigsaw. The kids are sat on the floor, playing a game"
That was the language I grew up with, and to use "sitting" instead of sat" would just have sounded weird.
I mean -- "the family is sitting down to dinner", sure -- that sounds normal because it is something they are doing. But if it is passive speech (so to speak) then why would anyone use "sitting"? It's just weird.
I am not even sorry.