/snip
For example, with regard to the Cleric class, the *mechanics* of the Channel Divinity feature says, ‘you gain the ability to channel divine power directly from your deity’, your polytheistic deity. This flavor has mechanical implications, such as if your deity is unavailable, displeased, or whatever. 5e especially blends narrative and mechanics. Consider how many spells are deeply rooted within the cosmological assumptions.
Note, I disagree with you on the point that the flavor is baked into specifically FR flavor. It really isn't. Kobolds as a slave race to dragons, for my favorite example, isn't a thing in FR and never was. This is something entirely new that they've bolted into the game. So, while I do agree that WotC added in too much specific flavor, I'm not convinced that it's specifically FR flavor. After all, none of the PHB races are specific to FR. There are no Avariel, for example. And dragonborn aren't a FR race at all.
But, on the specific point quoted, let's look at the exact text shall we?
5e PHB page 58 said:
At 2nd level, you gain the ability to channel divine energy directly from your deity...
Also note, on page 57 under Creating a Cleric:
Check with your DM to learn which deities are in your campaign
There is no mention of polytheism at all actually. Granted, all the examples are polytheistic, but, that's always been the case where examples are given. How is polytheism hard wired into the class in this example? Do you have any other examples?
Note, anyone playing D&D is going to assume polytheism anyway. Anyone with even a passing familiarity with fantasy genre fiction is going to assume that. It's something of an outlier to see monotheistic fantasy fiction. I can think of a couple, but, by and large, fantasy settings have gods, plural. Never minding all the real world myth and legend that serves as groundwork for fantasy fiction.
I'm not seeing how polytheism is hard wired into any given edition. Sure, you're going to have to rework the cosmology, but, that's standard practice in any edition when homebrewing. I mean, you had the Abyss and Hells and Outer Planes right there in both the 1e PHB and Monster Manual. And, considering virtually none of the 5e spells are original to the edition but are rather simply updates of existing D&D spells, I'm again somewhat at a loss to see how this is more of a problem now.