interestingly, 'accidental magic' is actually somewhat more impressive than what just-got-their-wands first years can do.

Harry (in cannon) performs accidental magic during times of high emotion and when he's not able to cast spells (ie, before he has his wand or summer vacations). This is also true with Ariana Dumbledore, Snape, and Neville in each other occurrence of accidental magic in the series. In HP:MoR, wizards use the mana/muscle system for magic. It seems likely that magic can 'build up' if unused and release in an explosive (sometimes literally) fashion in the form of accidental magic. Furthermore, since nobody seems to intentionally use it, it must have a drawback; extreme draining of magic disproportionate to the effects seems like a logical effect.

Interestingly, both Tom Riddle and Lily Evans were able to consciously control 'accidental' magic as children. They both ended up the greatest spellcasters of their year. This would further reinforce the hypothesis that it extremely drains your 'magic' muscle, given that working out one's magic has been established to make one a stronger spellcaster.