4e did try to be D&D... and failed in that regard... (actually it did not fail... but many believe so)
5e wants to be as inclusive and versatile as 3rd edition is. (And I appreciate the effort and I love what I see so far)
No, 4e tried to
redefine D&D. It stopped being what TSR through 2007 WotC defined as D&D and began using its language to define new idea. Some were good, some were not. The evidence of this is everywhere.
Tieflings going from "fiend-blooded mongrols distrusted by all" to "heirs of a fallen devilish kingdom with unified look and culture".
Eladrin went from being the celestials of Arborea/Mt. Olympus to a fey race resembling gray elves that exist on the feywild.
Archons stopped defining LG celestials and started defining elementals.
The whole cosmology was changed from the roulette wheel of alignment to the vast sea of planar places, the elemental planes got crushed into one.
Demons got redefined as corrupted elementals and the succubus bailed on them.
Giants were just baby titans; who themselves stopped being related to the titans of myth.
All elves became wood elves; primal and druidic (retconned a bit in Essentials).
Gnomes became escaped fey rather than miniature dwarves.
Many monsters got planar or elemental upgrades or additions; leading to the compoundword creaturename system of naming monsters.
Not all these changes were bad, but they were departures of the 30+ years of lore that preceded it.
Gary Gygax wrote an entire appendix to the DMG to say what the influences on D&D were. The famous
Appendix N. It
certainly isn't pure Arthurian Chivalric.
Appendix N isn't really the be-all, end all on the topic. This is especially true as Gary lost more and more control of it and other talented writers (Hickman & Weiss, Greenwood, Cook, Marsh, and Metzer) took over.
D&D is suitable for a variety of different playstyles and adaptations (from Ravenloft to Al-qadim) but its hard to argue the rules are suitable for adapting easily. Each setting TSR or WotC created (with perhaps the exception of Realms and Hawk) required major rewrites of the rules OR huge grains of salt to accept D&D tropes. (Look how something like Masque of the Red Death had to bend to create 1890's versions of the core four!). D&D is adaptable, but hardly generic.