Actually the sources are pretty clear in that the legionaries did not get in among the phalangites when the phalanx was ordered. Nor was the pilum of any apparent effective use. It is mentioned specifially to have been remarkably ineffective.
A lot of speculation is around as to why that was so, but generally it is believed thatte forest of pikes broke up the pilums so that only a percentage actually fell head first and thus posed a danger.

If a legionary had gotten in among the phalangites while the formation was ordered the formation would come to halt as they nearby men would have to drop their pikes to deal with him. That in turn would leave more openings, and rather fast, even if they managed to kill said legionary before he could kill anyone (best case scenario). It would be a quickly falling house of cards, yet whenever the Romans faced the pikes head on (ordered), it took hours to finish the battle.

The smallest attested units to have 'infiltrated' the phalanx was actually maniples, led by entrepeneuring centurions who reformed their troops to something more sensible and then edged into the gaps between tactical units. But only after the phalanx had begun to get disordered.
Had individual legionaries been able to infiltrate, the push of the phalanx would have staggered to a halt within half an hour as units tried to form up again, while others didn't want to advance alone. It would be a horrible mess terribly fast.

In any case the legionaries that faced proper pikeformations were not imperial legionaries with the 'lighter' twolayer shield that was actively used in melee. They were the legionaries of the 'Polybian' legion, with a larger curved oval shield, far too heavy to use in punching (I don't know about you but 22 pounds gets heavy pretty fast if you punch with it). The shield was a protable wall for them, and little more, of course it was better than the smaller shield the phalangites carried, but directly using the shield as you said would be near impossible as a doctrine (I suppose individuals now and then used such a move when in dire straits or something).