You're right, although in this specific context I think needing to refer to being 'sat' (or being stood, etc) happens relatively rarely and with context, you'd be able to work it out.
For example, if I tell you "I was sat on the sofa while we watched Netflix", and then in the next story I tell you "we had a visit from the police because I watch too many crime documentaries and they're suspicious I might be a serial killer - I was sat down and given a right talking to!" it's clear that in the former I was unlikely to have been placed there whereas in the latter, it's likely it was instigated by someone else.
Even without this context, if I wanted to make it clear, assuming I was a person who had no idea of the original meaning of 'sat' and just thought it meant what 'sitting' actually means, I would be able to clarify in a different way - "I was made to sit down" or similar. So although, granted, it's not as neat, we're not losing the ability to explain the concept - we're just doing it differently.
There are linguistic hills I'll die on (or at least get mildly injured on - I try and keep an open mind) but I love the way it changes.
One of the things I'm fascinated by at the moment is seeing the habitual be construction widen in usage - i.e. "She's crying" vs "She be crying". The former suggests she's crying right now, the latter suggests she's always bloody crying. Common in AAVE and apparently (having Googled to check I'd got the name right) in Hibernian English, but I've seen it creep out a bit more via TikTok/social media generally. What a useful, specific construction - technically, using the habitual present in 'standard' English, we could say '"she cries", but by itself it doesn't have quite the same feel and we'd be more likely to say "she cries often" "she's always crying" "she cries a lot". (There's another discussion there about bits of AAVE getting used when it's convenient but dismissed as incorrect the rest of the time, but it's still interesting nonetheless).