I'm under the impression it was the standard practice of Hellenic commanders in general and monarchs in particular to head the heavy "strike" cavalry wing - although given that unlike Alex they mostly fought enemies with by and large the exact same general army lineup, how the cavalry was divided between the right and left wing was anything but a foregone conclusion (Alex ended up just putting the heavies on his right, and leaving the left with lighter horse on the defensive). After all that way they had immediate control of the (hopefully) decisive "hammer blow" units, and the pike line could presumably do its primary job - holding the enemy infantry center in place - without close supervision well enough. Unlike the Romans the Hellenics tended not have staggered reserve lines of heavy infantry whose committing needed sound senior judgement, after all, although one would assume the assorted lighter infantry used for pre-contact skirmishing etc. would be retired behind the phalanxes and formed a de facto emergency reserve pool.

IMO the real major problem that plagued post-Alexander Hellenic armies was their general inability to rein in their heavy strike cavalry when the horse fight at the wings was won. The phalanx was formidable, but essentially a specialized linear attack formation and one that got into major problems in rough country and when its line got ragged (as almost invariable happened - didn't an entire darn Persian cavalry squadron slip through a gap in the line at Gaugamela ?) and generally not very good at winning a battle on its own, especially against enemy phalanxes. If the heavy horse went merrily off in pursuit of their defeated mounted opponents and did not remember to reform and come back in time, it could well happen that the phalanx might get routed by its peers, rolled up from the side if better-controlled enemy horse was victorious at the other wing, or something similarly undesirable.

Now granted, it was never easy to get cavalry to break off pursuit and reform after winning a horse fight. But if it wasn't achieved the hideously expensive heavy horse might well essentially neutralize itself from the battle simply by not being there, and more importanly would not be there to act as the "hammer" the Alexandrian combined-arms tactics pretty much required. This can only be characterized as unacceptably poor discipline that by and large defeats the entire purpose of the formations involved; Prince Rupert's heavy cavalry in the English Civil Wars, although by all accounts quite formidable as shock troops, had the same problem with ultimately disastrous effects. Comparable issues are known from other contexts as well; there was for example one Medieval battle where one side's knight smashed the militia infantry opposing them, and then duly scattered far and wide in pursuit - in the meantime the enemy's other "battles" were victorious and routed the rest of the army, leaving the knights looking mighty silly when they finally came back.