It certainly doesn't seem like that's the case for my daughter who's in some sense about half-way along that progression.
How would you know if it would be the case? What do you think are the traits of the English language that prevents your daughter from learning it faster?
Now, for sure, I have no very good reason to think that making prepositions less polysemic wouldn't be an improvement in actual use. But then I don't think you have any very good reason to think it would be an improvement for learners, either; it's just a guess, right?
Let's take the example of the 'bottle of soda'. Without looking at the particular case it seems for me hard to tell if there such a thing as an "empty bottle of soda" or whether bottle of soda means that the bottle is actually filled with soda.
That is not a problem if you regularly speak about bottle's of soda that might not be a problem. There are empty soda bottles but no empty bottle's of soda. At the same time if I search for empty bottle of soda in Google I get 37,900 results while I get 110,000 results for empty soda bottle.
Google Ngram is a bit stronger in favoring empty soda bottle but it still suggests that a sizable portion of people speak of empty bottle of soda.
In daily life you won't have much problems with that. Context will often be enough. If you however take a biochemistry book and try to understand what it's saying you often don't have the context to know sense of a preposition is meant. That means you need to spend cognitive resources to think through the possibilities that could be meant.
In English the polysemy of or produces problems when people get into mathmatical logic.
The Polish language has polysemy whereby ręka means both hand and arm. Can you imagine how that makes live harder any subject that speaks about the body whether it's biology or even massage?
The interesting thing is that the Polish culture had a lot of contact with languages that do have a proper word for hand that doesn't also mean arm. Why didn't they borrow Hand and Arm from German or English?
I suspect the reason is that ręka is too deeply imbedded in the Polish language. You can't just burrow a new word like you can add a new word for ketchup when the concept enter into the language.
I would suspect that basic prepositions are similar in the fact that it's very hard to borrow them from another language.
But then I don't think you have any very good reason to think it would be an improvement for learners, either; it's just a guess, right?
As a learner it's okay when there are a limited amount of prepositions. What you don't want as a learner is special rules. Saying "in January" while saying "on Monday" is an unnecessary special rule.
You want to have reliable rules that tell you whether there's a empty bottle of soda.
How would you know if it would be the case?
I don't know whether I would. All I know is that I don't recall ever seeing or hearing her have difficulty that seemed to relate in any way to such things. Perhaps I wouldn't expect to have done; I'm not claiming this as strong evidence; as I say, I think we're both basically guessing.
The rest of what you say still seems to me to be guessing that there "ought" to be a problem. I agree that you've presented some examples of ambiguity, and when something can mean X or Y and you want to say specifically ...
I'm working on a conlang (constructed language) and would like some input from the Less Wrong community. One of the goals is to investigate the old Sapir-Whorf hypothesis regarding language affecting cognition. Does anyone here have any ideas regarding linguistic mechanisms that would encourage more rational thinking, apart from those that are present in the oft-discussed conlangs e-prime, loglan, and its offshoot lojban? Or perhaps mechanisms that are used in one of those conlangs, but might be buried too deeply for a person such as myself, who only has superficial knowledge about them, to have recognized? Any input is welcomed, from other conlangs to crazy ideas.