In all honesty I'd expect the GA to be somewhat of a worry to passengers. They are a normal flight manoeuvre though I guess pretty rare to be honest as the extra fuel burn is not at the top of airlines wish list nor the crews'. Their rarity means most won't experience one ever (beyond training some pilots might not), and for that reason they cone as a shock.
As standard as they are they do present a higher workload and sadly in busy airports with s short taxi in the PA may never come. That's a shame but it's also a fact and not indicative of any laissez faire attitude towards keeping passengers in the loop, but quite often at the end of a sector the Red Cap is already in the door before the parking checklist is complete (I exaggerate, but only slightly). I think its a situation when the CC are well placed to speak up on behalf of the FC as they will be reasonably aware of what is going on from experience. Though the reason may bot be known to them you will be certain that if something is seriously awry you'll be getting some short sharp PA's.