I don't see why this shouldn't be the case. Surely children around the world don't learn to speak fluently by the same age?
It is obvious to anyone who only knows one language and doesn't know anyone who is bilingual that their own language is simple and other languages have varying degrees of complexity and ease of learning. For an English speaker, learning as a second language, French and Spanish are relatively easy, but Latin and Chinese are much more difficult and require each a lot of special extra studying to get 'right' (this is ignoring the irrelevant complication of writing method and living/dead situations).
But the question is about first language learning. It turns out from seeing many children learning their first language and from bilingual children that they communicate perfectly fine in any of their first languages and communicate equally well in either if bilingual. (I have no reference for this but) they are also grammatical to the same extent at the same age (French children know the gender of all the nouns they use, with mistakes made in false generalization just like English speaking children might make the mistake 'getted' instead of the past tense 'got').
Language like Russian or German with long lists of conjugations and declensions with multiple forms for gender, person, mood, etc, etc with agreement and then there are all the exceptions, they seem so complex and need lots of study by people whose first language doesn't have such features (actually, they need lots of study by people whose L1 -does- have similar features, they don't realize their own language is complex in that way and even if you know the form of the rules you still need to know the specifics).
It just turns out that first language learners have no problem with what others perceive as complexity. Think of all the separable verbs in English: call out, call up, call in, call off, put away, put up, put up with, put out. It's just not obvious which preposition to use for which meaning, you just have to learn it. But native English speakers don't even get taught this at school.
So, it just turns out counter to intuition that children do learn to speak fluently -and- grammatically in their L1 at the same rate for all languages.
Yes, as far as we can tell, all children without cognitive or social deficits achieve fluency at around the same age. Moreover, there is remarkable consistency in the order in which children acquire different features of the language. There is some variance between individuals, but that's to be expected.
Language is an intrinsic part of what makes us human, and the need to communicate stretches across all cultures and people.
I looked for evidence to back myself up here, but didn't find any, so here's a mere anecdote:
One of my professors who was working with the Menominee tribe in Wisconsin reported that, though the children seemed fluent at a young age to her, native speakers reported that they didn't consider children fluent until maybe 10 or 11 years old.
There are of course lots of caveats to this: Menominee is practically moribund (at best endangered) so the children were bilingual, and possibly reluctant learners. Who knows what criteria for "fluent" the native speakers were using (or my professor, for that matter). Maybe "fluency" is culturally related to "adulthood" in the native speakers mind or something.
Just thought I'd put it out there!
When talking about first languages, language acquisition is around the same age given freedom from cognitive disabilities and of course adequate exposure to the language (i.e. was not raised in the wild by wolves). However, language mastery is quite another story. As in the comment by @MatthewMartin, a language such as Cree which known to be notoriously difficult can take nearly until the start of adolescence to get a firm grasp on. I believe I heard this statement made by John McWhorter in one of his lectures.
To say that it takes longer for a healthy child to acquire naturally one language over another would implicate many more things than just sheer "complexity" of a particular language.
Let us make the assumption that for all natural languages, the expression rate of information is roughly equal; that is to say no human language exceeds another in how fast and efficiently information may be communicated via the language. If that were not the case, then speakers of languages with a much higher rate of information output (this is keeping in mind the economy needing in both coding and decoding a spoken utterance carrying some kind of meaning) would have an inherent advantage over language speakers with a lower output. All languages then would strive for the same strategies of communicating. But, as we see by looking at over the 5,000 uniqe languages of the world, that is not the case at all! There exist many many strategies to communicate over roughly the same meaning, each one with their own benefits and strengths which in the end should equal out to the same rate of information flow for every language.
So, if one accepts that language speakers communicate at the same rate regardless of which language they may be using, then why should one language take longer to gain fluency in than another? As said previously, different areas of language may be acquired sooner than others, but any difference should be minimal. The linguistic idea behind this is that all languages are equal and equally complex. We are only biased by our own native toungue(s) and the languages which we have learned as L2s, so yes indeed one might think a child would take longer to acquire say Latin than English but it is more of a subjective fallacy.
It does seem to be true however that there has been a general trend in language to "simplify" itself by removing case inflections, verb-subject agreements, etc., but this may just a subpart of the cycle of language change itself. Nonetheless, that would be a related topic to research which might shed light.
It sounds like a matter that needs more study. It is plausible that most natural languages have nearly the same objective complexity (which could be defined variously, e.g. lexicon size + amount of morphological/inflectional rules), so that children earn proficiency at similar rates for most natural languages. But what if a child's L1 were an objectively simple language such as Ido (or Esperanto)? Has acquisition rate ever been studied for such a scenario?
And note that it is difficult to tell how well a child is acquiring language, because the ability to speak comes more slowly than the ability to understand, and perhaps more slowly than the mental ability to form sentences. It strikes me as difficult to tell how much a pre-speech child comprehends what has been spoken. Pre-speech toddlers can be taught baby sign, which you might use to tell how well they understand speech, but I wonder if having learned a sign language might speed up speech acquisition (thus biasing your study).
The way you worded your question implies some kind of comparison. We can't really say that acquiring Russian aspect is harder or easier than English tenses or Latin declensions. What is easier, learning Cyrillic or cuneiform or devanagari? You can only answer this question from the point of view of an L2 learner. In the case of L1 acquisition, it's all the same. All languages are learnable since their primary goal is communication.
If you need references, I suggest you start with "Crosslinguistic and crosscultural aspects language acquisition" (pp. 219-224) in Fasold & Connor-Linton (Eds.), An introduction to language and linguistics. After that you might want to have a look at Lust's Child language or Bavin 1995 review article "Language acquisition in crosslinguistic perspective" in Annual Review of Anthropology 24.
My unqualified conjecture is that a language would evolve to be easy to learn, especially in a pre-literate society. If the rules are too complex for a child to learn, the complex rules will eventually be destroyed by repeated failure of people to assimilate and follow the rules.
I think my view is pretty consistent with the theory that there is a universal grammar that all languages follow. All languages evolve to be ones that a child can master, based on a humans natural language to understand grammatical rules. I would add that languages can acquire some variance and some complexity, but they have to be master-able by children to survivor.