Look, I'm really at a bit of a loss here as to how familiar you actually are with 4e. Some of your posts have a tone which suggest a high degree of familiarity. Others make me think, as Hussar does, that you don't know much about the system at all.So all classes don't have a power that can "push"? If they do, then that taste is lost.
So I can't tell if the question I've quoted is meant to be rhetorical or not.
Assuming that it's not, then the answer is: all PCs have access to the Bull Rush power, which allows a STR-based push that deals no damage. The sorts of PCs from the PHB who are likely to have a STR that makes this tactic have a viable chance of success are some Clerics (melee-based ones), some Paladins (non-CHA based ones), Fighters, some Rangers (two-weapon ones), some Rogues (brual scoundrels) and Warlords. Most of these would have some access to class-specific powers with generally better forced movement effects (often combined with damage). I think Fighters would probably have the best such access, as they tend to be the most controller-y of the weapon-using classes.
So the fact that all classes have access to a power that can push (namely, Bull Rush), and that a number of classes might be able to make good use of that power, and that most of those classes might also have access to class-specific powers that grant forced movement, doesn't change the fact that, in play, the different classes play pretty differently, giving rise to interesting tactical options.
The party that I GM has a polearm-wielding dwarf fighter, a generalist wizard, a drow sorcerer, a cleric|ranger-archer and a CHA paladin. In combat, the fighter is the most obvious controller, using a combination of reach and forced movement to shape the melee situation. The paladin tends to hold the line and lock up one foe (or sometimes a few foes for a brief period) - but while he can mostly soak their attacks (through a combination of marking and immediate actions) he can't control their movement very well. He also does some healing and buffing. The wizard tends to make ranged attacks which are a mixture of multi-target damage and control, including some terrain effects, teleportation and dazing. The sorcerer can operate both at range and in close - he uses his drow darkness ability to shield him and grant combat advantage, and does a lot of damage with a little bit of secondary control (including a little bit of forced movement). The cleric|ranger's main function is to do damage with bowfire, and he also does some healing - more than the paladin, but not a huge amount more.
Now of course, in any given combat, the paladin could try bull rushing, the wizard could try punching enemies up close using fists, the ranger could draw a sword (he carries two, and has a reasonable AC) and charge into melee, etc. But it doesn't happen. Each PC is built to emphasise certain strengths and weaknesses. Some of that is determined by class selection, and some by subsequent power and feat selections. The PCs don't come across remotely the same at the table, even though all have at least some access to forced movement powers.
That's not to say that sometimes strange things don't happen. In the last session a combat started in which the sorcerer ended up holding the front line - due in part to an attack from the rear which left the paladin in the wrong position, and in part because the fighter was down to about 20 hp with no surges left, and hence was hiding in the middle of the party attacking with reach over the sorcerer's shoulder. One time, the wizard not only got an opportunity attack (using his Tome of Replenishing Flame as an improvised weapon) but he hit and critted on that attack, and therefore actually killed the monster in question (I let him have the +2d10 fire damage from his Tome, on grounds that when you crit with a Tome of Replenishing Flame as an improvised weapon it has undoubtedly burst into flame in the face of the enemy.)
But when things are going optimally for the party they are not relying on the wizard to kill things in melee, or on the paladin or archer to be in charge of the forced movement.
(And in case someone comes in to say that PC differentiation applies only in combat, I should mention that the PCs are very different in skill challenges also - the wizard a scholar and diplomat, the paladin a diplomat and priest, the sorcerer (a DEX/CHA build) a manipulator and sneak, the fighter a tongue-tied and ignorant athlete, and the cleric|ranger a wilderness scout. Which is not to say that the dwarf doesn't from time to time find himself trying to bluff or be diplomatic. It's just that when those times come, it tends to mean something unexpected happend to throw the party of their standard operating procedure.)