Actually, IMHO, the biggest offender BY FAR is the cleric. Spellcasting clerics are found only in D&D and D&D-inspired fantasy settings.
I disagree, but to the same extent you could make that argument, you could also argue that magic entirely without a religious component is found only in D&D and D&D inspired settings. The vast majority of magical systems in history have involved invoking the power of some sort of god, even if that god was a bit smaller of a god than the word has come to mean for us. The notion of natural magic without religious or spiritual component is very modern.
The assumption that the arcane does not have anything to do with the divine makes the same sort of forcing assumptions about Wizards that it makes about Clerics, only in general, the people that complain about it are perfectly happy to not have all their Wizards be witch doctors and wizard-priests.
The class almost requires and active polytheistic pantheon of dieties that dole out powers to their followers.
No it doesn't. The primary inspirations for the Cleric came out of a monotheistic tradition, which is precisely why - other than for reasons of game balance - D&D has an arcane/divine split. If you look at the list of 1e Clerical spells - create food and water, part water, raise dead, remove disease, insect plague, sticks to snakes, flamestrike, etc. - it is not coincidently almost entirely a description of miracles recounted in the Bible. Moreover, the flavor of the Cleric as armored warrior is taken primarily from the Song of Roland, right down to the original prescription that the Cleric not used edged weapons.
Also, it assumes that the setting has a militant religious order.
Yes, this it assumes. But it can be assumed that if the setting doesn't have militant religious orders, it probably also doesn't have adventuring clerics.
I would rather have a more generic spell casting class that is not required to be tied to a religion or philosophy.
In other words, you'd like to have a spell casting class primarily inspired by the D&D Wizard.
Why can't arcane magic heal? Why should a setting assume that there is this dicotomy? Also, why are clerics allowed to wear heavy armor and carry weapons, while the "other type" of spellcasters (wizards and sorcerers) have almost no proficiency with weapons or armor?
Most of these questions can simply be answered with 'game balance'. Initially, spellcasters dominated the game. The solution that was adopted was to make spellcaster heavily restricted in various ways.