Running off the side of the runway may not be a big deal, particularly where the edge of a runway is just a white line in the grass and you're going quite slowly by the time you cross it. If you're well below take-off speed then a go-around sounds like it might sometimes be a worse option, as might bending the undercarriage in a desparate attempt to regain the centre line.
Running off the side is, however, a reportable incident, I discover. (Several years after having once done it and not told anyone.)
Hmm. I guess it's one of those things where one has to make a judgement when it happens (accept running off; steer back onto the runway; full power and go-around). At a point when one's confidence in one's judgement is already iffy due to having just screwed up the landing.