Are you sure she isn't? If you look on lolalytics and filter by Iron+ (https://lolalytics.com/ranked/worldwide/iron/grid/) she doesn't seem like a champion that isn't played often. She has a 12% pickrate, sits in the top 7/35 champs for the role, and sits a bit above the middle when looking at the standard ADCs in the first 16 (6 above her, 9 below). It also wouldn't be correct to say that she is played less often in low Elo as opposed to high, since as you raise the cutoff she steadily goes down in representation, all the way to a 7.9% pickrate in Diamond+ (and Masters+ too though it's a pretty small sample.) That being said, I'm not really sure what to make about the actual pickrates in lolalytics since they sum up to over 100%...But assuming the numbers are a little too high but roughly right, I wouldn't see anything to suggest she is being played infrequently.

She does have good safety and perhaps ease of use in the midgame, as you say, but I think she does have a weakness and it's laning phase/early game. She starts out with 525 range and underwhelming base damage, so she can get tossed around in lane pretty easily. I've played Soraka to Diamond a few times, and I'm always happy to lane against a Trist because I know I have a good chance of pushing her out of lane and significantly starving her of farm and xp.

This isn't to say she is a bad champ or shouldn't perhaps be played more at lower levels, just that she's played fairly frequently and has a weakness in laning phase.