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.
There is no such thing as "active feats" in the rules
In theory, you can declare to use as many feats as you like at the same time, provided they are compatible with each other.
A simple example of incompatible feats would be Rapid Shot and Power Attack. The former applies to ranged attacks, the latter to melee attacks, so you can't (normally) use both at the same time.
Other combinations of feats are far less obviously incompatible. Let's take a look at Power Attack, Vital Strike and Greater Cleave, since you mentioned it in your question. Power attack simply requires making a melee attack. Vital Strike and (Greater) Cleave are problematic however. The feat descriptions state
When you use the attack action, you can make one attack at your highest base attack bonus that deals additional damage.
and
As a standard action, you can make a single attack at your full base attack bonus against a foe within reach.
respectively. Vital Strike requires you to use the Attack action, which is a type of Standard action that involves making a melee attack. (Greater) Cleave is another Standard action type altogether, meaning you can't use both at the same time. Assuming you are using a melee weapon, you can combine either with Power Attack though.
Best Answer
Bear traps aren't really a trap
A bear trap is not the same as a trap created using the Craft: Trapmaking skill, in the same way that scattering some caltrops in a hallway doesn't count as a trap - both are ready-made items that anyone may purchase and use - and both are far less effective than an actual crafted trap.
In-fact, calculating all the CR modifiers of a bear trap yields either 0 or -1 (Disable Device DC for the trap is 20, which gives a 0 modifier, but the description specifies that it may also be safely disabled with a stick - so the DC is effectively lower, meaning a -1 modifier). The rules for planing a trap specifically state:
So, such a bear trap wouldn't really count as a trap.
What you may be missing
Hope this helps.
As an anecdote, I'm quoting here the full description of the CR 1 encounter which is the source of the 12 bear-traps = CR 1 trap notion. In my opinion, this is just a CR 1 encounter, not a single CR 1 trap...