Why not? "I wasn't entirely happy with the approach, so rather than take a chance I thought it better to go around again and get it just right."
I've been on at least two flights where the pilots did go arounds, so I'll give you my viewpoint as a lowly SLF.
The first one was a night approach to BOS in relatively poor weather. Shortly after the go around the pilot announced something to the effect that they didn't like the way things were lined up for that approach, so they elected to go around. There was no panic in the cabin and I wasn't in any way concerned. Nor did it reduce my opinion of the pilot. In fact, I appreciated his caution.
The second go around was an evening approach to ATL on an L1011. We were quite low -- low enough that I was looking into the doors of the Delta maintenance hangers off to the left of the runway. I was in first class, too far to hear the engines spooling up. But I noticed the angle of attack increasing, greater than what I expected for flare. The gear never touched the runway, but I'd guess we were pretty close. The pilot came on and said that an aircraft had not completely cleared the runway. I was more concerned about this incident, than the former, but again not terribly worried.