As a controller in a very similar vein to Heathrow Director, I've had many go-arounds. The whole point of them is to stop the inbound plane from landing on the outbound plane, or an inbound plane from landing on the previous inbound plane. Now for some basic maths, brace yourselves..... An inbound aircraft on the approach to a runway will be doing approximately 3 miles a minute. This means that with 3 miles spacing between inbound aircraft, the front one would be touching down as the next inbound was at 3 miles (approximately 60 seconds away). If the front one were to stop and remain on the runway then the next inbound would be up his chuff in 60 seconds flat. Now take into account the fact that sometimes runways are wet, sometimes pilots miss turn-offs, sometimes there is windshear, sometimes inbound aircraft don't fly the correct speed, and then you have a situation requiring a go-around. These things will always be "seconds apart" because as stated above, 3 miles between aircraft is literally 60 seconds, which even the dullest of people will realise does not give a huge amount of leeway!!
All this sensationalist c**p ends up doing is giving the ordinary person the impression that a go-around is suddenly a life-threatening situation, whereas in reality it is the life-saving situation (i.e. not bumping planes together). This is where some of it comes down to the crews on the flight deck.... The passengers should be told that this is a normal, non-threatening, completely safe procedure, instead of them leaving the aircraft thinking that they've just nearly ended up at the pearly gates!!