Eh, The Lord of the Rings may have started that way but by the time it was finished it was definitely its own thing, a "mythology for a new age" style of whossname in an era (post-WWII) where we really had no defining cultural mythology (I'm separating "culural mythology" from "religion" here because of social factors that I'm not sure we're allowed to talk about. It's a common thing in writing that the finished product is wildly different from the original intent, to continue with the Middle-Earth example it was originally going to be a "mythology of England" that had been lacking compared to the Continent.
Your suggestion here is the exact opposite. Tolkien's earlier writings and various notes (The Silmarillion, the Children of Hurin, and so on) were intended to be his mythology. The Hobbit was intended to be a standalone story in its own little world with little need for backstory - it was intended to be a children's bedtime story written for his kids, after all. He later decided to incorporate The Hobbit, and later Lord of the Rings, into his already established mythology when backstory started to become important (There's references to Gondolin in the Hobbit, for instance).
You look at his entire mythology (this takes one hell of a lot of reading) and you'll find that it's pretty complete. He has references to an End Times, and the way it plays out is awfully similar to the Norse legend of Ragnarok, with a sprinkle here and there of Greek (the constellation Orion is dealt with) and Christianity (Morgoth is Satan, rather blatantly). Considering this, it's much more likely that Lord of the Rings and the Hobbit were standalone stories and his myths were added to create a greater synergy with the rest of his writings. It's much easier to imagine everything in a single world of your own devising, than having to keep track of everything in multiple little worlds.