[RPG] n official explanation for the difference in duration between Infernal Healing and Celestial Healing

The best way to judge what classes should have access to a spell is to compare it to the kind of spells those classes already have.

Wizard and Sorcerer compulsions tend to be forceful in method and drastic in effect: The examples you gave describe subverting the victim's normal mental process by forcibly inserting a foreign thought, and blatantly stealing control of the victim's mind.

Clerical spells, on the other hand, tend to use more straightforward methods of achieving their ends, and often express the role of clerics as spiritual leaders: Thus, the spells that allow them to speak with authority and be obeyed.

As for why the power of Power X isn't compelling... Well, if you look at the ecology of gods as described in, for example, the Planescape setting, belief is the food of the gods - without it, they lose strength and eventually starve to death, or at least enter a state that is for most practical purposes equivalent to death. A follower who only vaguely follows their patron deity's teachings is still more faithful, and therefore more valuable, than an unbeliever magically compelled to serve. Of course, individual gods might have a thing for magical compulsion, but that's not enough for something to get included in the standard priesthood package.

Oh, and like mxyzplk suggests, there's more game design-y reasons for it, too: if Clerics were good at all forms of magic, they'd be far superior to wizards, even enchanters - and playing an enchanter would be much less interesting.

Armor bonuses are more common than shield bonuses.

Mage armor provides an armor bonus to AC, which doesn't stack with other armor bonuses. Since nearly everybody has an armor bonus (even proficiency with light armor gives access to mundane options that match the +4 bonus), this has a limiting effect on its usefulness to non-caster classes. This is why the spell is allowed to be cast on anyone and to last so long: it's not as useful so opening up the target range doesn't have as big an impact on balance.

Shield, on the other hand, provides the much less commonly-used shield bonus to AC (many fewer classes have this proficiency, even fewer of them usually take advantage of it, and getting a mundane shield with a +4 bonus is a build-defining choice). Very few classes run around with a +4 shield bonus, so even those who do use shields would find it very useful... and thus its availability is limited to the caster, to keep that usefulness in check.

It's the same reasoning that makes rings of protection (deflection bonuses) cost twice as much as bracers of armor (armor bonuses) with the same AC value: the less common a bonus is, the more valuable it is because it's less likely to conflict with another existing bonus (which would make it useless).

Two asides

1. It's worth noting that mage armor and shield are both force effects, which have various usefulnesses, but that only shield stops magic missile. It appears Wizards overestimated the value of direct-damage spells, and underestimated how easy ranged-touch-attack spells would be to land, so they thought magic missile would be a cornerstone of wizards everywhere. If that had been true, shield would be much more useful--making its duration/target restrictions more sensible.

2. Exactly how bonuses stack (especially as regards armor bonuses and enhancement bonuses to AC) seems to be rather murky and contradictory in the rules, so if further clarification is needed on that particular aspect of this issue, it should be made a separate question.