Not all runways are 2200 meters tarmac.... and I wouldn't rely too heavily on the brakes of the average training aircraft.
So yeah there's no limit to how low one can go around, sometimes it can be with all wheels down having realised you won't stop before the fence
And I would say that sometimes ATC will have to override the cockpit decision making. Runway incursions are not unheard of and sometimes angle/slope/sunglare don't make them too easy to spot.
Ivor