RP-wise, cleric spells are not spells*. They are prayers fulfilled by deities. A deity is not an idiot, and would know the tadpole is there. Nothing drags a god, kicking and screaming, into resurrecting that irritant.
No, they are spells.
Deities provide the powers to their subjects. Which they can then channel in whatever way they wish.
If what you said was true, it'd be impossible to break a vow with a deity by using their spells for things against their teachings... But this is and always has been possible. As is the case for Paladins and Druids too, whom also get their abilities from higher powers and as such, can lose them by using them improperly (Less so in 5e with changes made to remove aspects of this, with only Paladin's oaths being left as a way to mess with your powers when broken. Prior editions had Druids with strict alignment requirements as well as strict equipment requirements)
Cleric spells are basically just like Arcane spells, only you have a deity as a gatekeeper for access to the "Weave" that powers them. If the deity likes you, they give you access. If they dislike you, they revoke and prevent access (But another deity might step in and give you access instead). With most Cleric spells being general "Deity Power" type things, and then you have the specific Domain spells that are unique to a particular deity (Based on the domains they are associated with)
If a Cleric casts Revivify, it's not them saying a prayer to their deity and the deity going out of their way to go and do something (As you say, nothing drags a god, kicking and screaming into doing anything. Gods do as they wish and many, especially evil ones, don't care a whole lot about the affairs of mortals - Let alone a singular specific one. Heck, even a deities "Chosen" is barely looked at by said deity). It's them simply accessing the divine power of a deity to cast a spell.
Which is no different to Arcane magic, whereby the weave is accessed and channelled to form spells (Either naturally such as for Sorcerers, or by studying it for Wizards) - Which incidentally does have Mystra as a guardian that can limit access (Hence the whole Gale backstory) while Mystra is also a deity who can provide divine power for Clerics. A thing that has always struck me as odd, that she wouldn't provide her clerics with access to the weave in lieu or in addition to the divine power (Though, I suppose this is game balance things having free Wizard/Cleric dual class from a deity choice would be unbalanced)
As for Witches being evil, they are under the same scrutiny as Warlocks. That is their source of power is often a pact with an evil entity, which causes concerns for the same reasons why a Cleric of an evil deity does, they will have to act in accordance to said evil entity to retain the access to powers (With pact based sources often being stricter due to contract terms - As seen with Wyll, who's thing was trying to use this power from an evil entity for good but was manipulated into doing evil due to the contract). Witches also use curses which are not particularly "Good" types of magic, which also adds to their infamy.
