"Imagine: it is another place, anoter time. The world is much like ours was, long ago, with knights and castles and no science or technology - no electricity, no modern comforts of any kind.
"Imagine: dragons are real. Werewolves are real. Monsters of all kinds live in caves and ancient ruins. And magic really works!
"Imagine: you are a hero, a famous but poor adventurer. Day by day you explore the unknown, looking for monsters and treasure. The more you find, the more powerful and famous you become.
"Your home town is just a small place with dirt roads. You set off one morning and hike to the nearby hills. There are several caves in the hills, caves where treasures can be found, guarded by monsters. Adventure awaits!"
The preceding is cribbed, almost word for word, from the introductory couple pages of the 1983 D&D Basic Set. And to my mind, that's the only kind of "implied setting" the game needs. Tell us it's a world like ours was, long ago, with little technology and where monsters are real and magic works. The rest can be left up to the DM.
Now, a couple basic assumptions have to be made when you design monsters, like "goblins are bad." Or "drow align with spiders." But beyond the well-established legacy stuff, leave it alone. Let it be defined when you publish an adventure. 4e had some fun with faeries, but they tried a little too hard to shoehorn a particular view of the world down people's throats. And that's said as someone who LIKED a lot of it.
Religions and cosmology are probably the thorniest problem, because you have a class or two (clerics and paladins) that implicitly are tied to gods. But I think it would be best to throw in a few (small) sample pantheons, like, say, Greek, Norse, PoL, and Greyhawk. Mention you can use one of those, create your own, or just ignore it completely and have characters serve a particular philosophy, like "good and law." Keep the channel divinity feats generic based on spheres of influence (good, law, nature, war, weather, etc.) and call out those spheres for the example deities. Yeah, it's a little more work, but in the end, it's probably more useful to the average gamer. Since it's natural that an individual deity might offer a unique power, you could include deity-specific channel divinity powers in setting books down the road.
As far as art goes, I don't want to always see the "same world." Elmore always managed to depict evocative clerics without being precisely clear on which deity they served. And when it comes to adventures, tie them to a town or a world location without saying exactly where that town is. All of the classics did this, from The Village of Homlet to Keep on the Borderlands, from Castle Ravenloft to Expedition to the Barrier Peaks, and from Against the Giants to The Sunless Citadel.
That kind of handwaving works, and works well. Sure, if you want to put the Hand and Eye of Vecna as examples of artifacts in the DMG, go nuts. That kind of stuff is evocative and interesting - and easily ignorable by those who don't want to use it.