Ah, but the goblins also have similar considerations - it may be silly for a dwarf to get in a wrestling match with a goblin when 9 other goblins are rushing in... but it may be an *excellent* idea for the goblin! All the goblin has to do is hold on while his buddies poke holes in the dwarf.
Anyway, all this to say that I'm not too bothered by dwarves bitting, kicking etc, because I know how random and chaotic sword combat can be, and that at some instant, *not* using your sword (axe etc) is the right thing to do.
The goblin would only want to if there were not 9 other dwarves ready to jump in as well. 10 goblins against 1 dwarf is MASSIVELY different from 10 goblins against 10 dwarves. In the former case, yes, the goblin would wrestle. The latter case? No, or at least not as a first choice - he might if he was disarmed or his weapon broke.
Real close combats in battle were NOT usually every man for himself, if the army was remotely disciplined, since soldiers usually want to survive far more than they want to kill the enemy. Instead, soldiers stayed together for mutual protection and picked the easiest fights. They would not get too focused on one foe in case his comrade intervened. This applied to both sides of the combat. Look at the Romans - their sword combat was very bloody, somewhat chaotic, but not random, and they usually beat foes who did not understand this. The same could be said of hoplite battles or the spear formations of the early Muslims. In fact, in all these cases, most deaths usually occurred after one side ran away - the tight formations led to few deaths during the main phase of combat. This is true for most battles at the time, where most soldiers who died died while routing, not while opposing the enemy.
Battles, except between completely wild barbarians, usually involved a lot of teamwork and soldiers protecting each other. They were not like DF's individualistic encounters. Wrestling did happen, but it was usually a second resort after a weapon broke, the enemy closed to very short range or something similar, and prolonged wrestling matches were rare indeed, with one party dumped on the ground and finished fairly quickly.
Biting someone in armour will usually only result in broken teeth. Kicking, punching and wrestling can do damage and be very useful for single combat, but in battle it is generally better to just stay in formation and try to break the opponent's.
Before you think I am trying to dismiss wrestling, I am not - in a 1-on-1 armoured duel, or a dogpiling situation as you described, it is a massive part of combat and very useful indeed. In fact, in an armoured sword duel, wrestling and half-swording are the main tactics. It would just not be the first tactic for battle.