Yeah, I don't think a biome as an entrance is a good idea.
Think of the current dimensions. The Nether requires obsidian, which requires lava and water, both of which can be found everywhere. The End is definitely dependent on luck to find on your own, but there is a way to track them via Eyes of Ender (there is some luck required to make them, as finding Endermen and Blazes can be a bit difficult, but in most worlds both are easy to find). A biome would be incredibly luck-based, especially with current biome generation algorithms involving temperature, and would be incredibly frustrating to find (imagine if finding a woodland mansion was required to get to the End, and there were no cartographers). Not to mention that a new biome would change the world generator, resulting in a visible seam between old chunks and new.