FWIW
I've had 4 GAs as SLF (and a few as the PIC in lighties). It's always interesting to observe the reactions from the other pax. These range from sheer terror to absolute disregard. I'm sure that the former grouping are, shall we say, "nervous" passengers while the latter are likely dead-heading "front seaters". Much of the concern comes, in my opinion, from two factors:
1. Go-arounds are relatively rare. A guess would put them at well under 0.1% - that under 1 in a thousand.
2. Too many folk, especially our nervous pax, have watched and treat as 'the truth' the depictions we continue to see of aircraft falling out of the sky in material coming out of Hollywood and the like. (How many aircraft fell out of the sky at Y2K?)
On a couple of GAs, the flight deck explained what and why.
On another, after the (successful) second attempt, the skipper explained on the PA that the 2IC had done the approach, was still in training and hadn't done the approach correctly, so he (the skipper) made him do it again.
I should add that the skipper's humour was appreciated by the pax, all of whom were active aviators. The aircraft was a DC3 and the flight was a "nostalgic joy ride".