In the last 3 companies I have worked for - types being Atr42, 146/rj and 737, the SOP has been the same. Once established on either localiser or vor inbound, set missed approach heading.
This may be quite different to the inbound track.
I have always set it on the basis of expected drift in the missed approach. Then on the go around, just press 'hdg sel' at the appropriate time. Even if the heading change doesn't occur until say 1000ft, everything happens so quickly on a go-around, that the 'escape' heading may be more appropriate. Most pilots are quite capable of tracking the runway, or monitoring the track to 1000ft or so, but the heading change could easily be forgotten in the heat of the moment.
NDB appoaches are of course different in that you are using the heading bug constantly to 'drive' the aeroplane along the desired track and so can't realistically set missed approach heading until at the MAP. And if you are flying manually, say in a raw data ils or localizer, I see no reason why you can't use the heading bug as you personally prefer for orientation. Whether to use your support pilot to manipulate the heading bug or d.i.y. really depends on commonsense - personally if I am PF, I prefer to make small corrections myself. Oh, the arguments I had with one anally retentive checkie about use of heading bug!