Common wisdom appears to have it that parties in B/X transition from pure dungeon adventures at 1st to 3rd level to the wider world of wilderness adventures after reaching 4th level. The Expert Set adds rules for characters of 4th to 14th level and rules for wilderness adventures. And of course B1 In Search of the Unknown and B2 The Keep on the Borderlands are the most classic dungeon adventures and X1 The Isle of Dread was the first D&D hexcrawl. So obviously it must be true. Basic characters stay in the dungeon, Expert characters expand outdoors.
But I’ve come to wonder whether this really is the intention behind the way rules are split between the Basic and Expert Set. My suspicion is actually that the choice to split the rules into multiple sets was done with the intent to introduce both players and GMs to the rules gradually and not overwhelm them with everything at once. Which I think might have been a pretty good choice. The original Basic Set was a total of 60 pages. The Rules Cyclopedia comes to 300. That’s a lot of stuff to digest in one go before you feel confident that you know what you need to start playing. If you want to teach the basics of the game, you do need the dungeon, but outdoor adventures are indeed something that can, and perhaps should, wait for a bit later. Once everyone who is completely new to the game has got the hang out of the basics. By putting level 4 to 14 into the next set, the amount of spells that players (and GMs) are exposed to is much easier to overlook and you also get a collection of monsters that for the most part wouldn’t be absurd to face for a new beginning party. (Looking at you here, Dragon.)
I suspect that the separation of content was done as a teaching aid, primarily for GMs. It’s not so much that adventures change at higher levels, but that GMs can expand once they have become familiar with the basics. When you look at the Expert Set it says that “now” new paths of adventure are open, but does not do so in the context of character level. It is “now” that the GM has access to these expanded rules of the game. The Rules Cyclopedia does not touch upon this whole subject at all, from what I was able to tell.
Another strong piece of evidence, as I see it, are the modules B10 Night’s Dark Terror and X1 The Isle of Dread. Terror is a Basic module for characters of 2nd to 4th level while Isle is an Expert module for characters of 3rd to 7th level. Both begin at Basic levels and continue up into Expert levels and they are both wilderness adventures. The creators of these modules clearly did not write under the assumption that “you have to be this high” to go on adventures in the wilderness.