Peiper hit the weakest held section of the front in the north (a single mech cav battalion with jeeps, armoured cars and light tanks) and then rolled through the gap between two US corps. He could not have wished for a better opportunity. That they got as far as they did was remarkable enough. The last thing they would have wanted was to get involved with the fighting on their right with US 2nd and 99th Divisions (and potentially the US 1st Inf). Had they gone north the US 1st, 30th Infantry, 3rd Armoured and 82nd AB, could have filled in the gap, blocking approaches to the Salm and Ambleve River valleys and stopping any further drive west at all, in effect blocking 6th Pz Army's advance entirely. Had he turned south into 5th Pz Army's zone he would have jammed up the roads there and the same US divisions plus 7th Armoured would have come down from the north, again sealing the Salm River crossings and likely being able to build a line along the Ourthe River north and west of Houffalize. End result here would likely have strangled 5th Pz Army's 58th Pz Corps drive west in support of 47th Pz Corps (2nd Pz and Pz Lehr), the troops that actually did drive to the very approaches to the Meuse.
As it was Peiper's penetration compelled the 30th Infantry, 82nd AB and 3rd Arm'd to deploy over a stretched front for most of a week. This penetration, combined with the attack on St Vith and the penetration past Houffalize by 116th Pz (58th Pz Corps) forced the abandonment of the St Vith salient. His presence in the Ambleve Valley allowed 5th Pz Army to exploit the actual breakthrough in the centre while five allied divisions were tied down between St Vith and Stoumont.
Any additional success by the Germans in the Ardennes could not have come in the north, the terrain and road net mitigated against quick movement west and too many American troops were on hand to quickly reinforce V Corps' right wing. The Germans only hope of reaching the Meuse and causing the allies more heartburn was in the centre with 5th Pz Army, where more was achieved with less in more open country by divisions that were, quite frankly, better quality than the Dec 44 SS divisions. The German attack was going to fail, the most that might be expected was they extend the battle past mid-January by throwing their weight behind 5th Pz Army earlier,....but that is too is questionable.