The tactic is quite risky. A determined enemy can counterattack against the infantry on the flanks, thereby cutting off the spearhead from resupply and quickly bringing it to a halt. In order to avoid this the spearhead must move as fast as possible in order to keep the defense from re-organizing in this fashion.
The first use of an armored spearhead was during Fall Grelb, the German invasion of the Low Countries against the British and French armies. Surprising them out of the Ardennes forest where "obviously" no armored force could operate, the spearhead quickly started running for the coast at Dunkirk. The French and British armies were split on either side on the German forces, and at one point attempted to cut the line with an armoted attack on either side. The resulting Battle of Avaranches was very close to being successful, but a lack of radios or other communications made the attakc slow.
Only a few years later new tactics had been developed to effectively deal with the concept. The basic idea was to throw small units in just at the corners of the spearhead, making them avoid combat instead of slowing down to engauge. By doing this repeatedly you can narrow the front of the spearhead until it no longer commands enough width for the following infantry to effectively move. When the Germans tried the same tactic again in 1944 during the Battle of the Bulge, the US Army was able to very quickly "pick the corners" in this fashion and brought the spearhead to a halt in a few days.