Why?
(I like your interesting linguistic comments. Take it as a lowbrow provocation.)
Because at the end of the day, the purpose of a language is for it to be learned and spoken. It's not a conlang made by some dude in an armchair mashing together the oddest/most obscure examples of phonemes, syntax, word order, morphology, and alignment they can think up to form the most interesting language 5everr. Natural languages are strictly utilitarian. If they were so difficult that they would baffle even people with 150 IQs they would have ceased existing as languages long, long ago.
It simply needs to be remembered that Magyar is a real language spoken by real people every day. Mystifying its complexity like the above gets away from that in service of exotifying the Thing and, by extension, to some extent dehumanizing its speakers. It's certainly not what you're doing explicitly, but it comes across as the subtext, and it's kind of gross.
All languages exist to serve an equal number of use-cases for an everyday speaker, and so will have a more or less equal amount of complexity in terms of semantic inventory size and grammatical complexity. What you're commenting on, really, is weirdness relative to English. Because, yes, Magyar has an assload of cases, and reading about them can seem extraordinarily complex to someone without a lot of linguistic experience. But that complexity is equalled in pretty much every language in some area or another. Think about the amount of complexity which exists in the nuance of English word order, or preposition and particle usage, or tone, to a lesser extent. They're all different answers to the same question of "how do I organize the world into units of content understandable to the person I'm communicating to. It's 5 = 1+1+1+1+1 vs 5 = IIII and I vs 5 = 3 + 2 rather than 5 vs 11 vs 19.
But also, like I said. When we're talking weirdness relative to English. It's not
that weird. Any language which doesn't: a) use tones or ejectives, and b) uses an N-A alignment just doesn't seem that weird to me on an absolute scale.
Is there a phoneme, or more than one, in Danish that is practically impossible for English/German/Slovene speakers to produce?
It seems that extreme grammatical differences are difficult to learn and reproduce well, even if they're at least possible. I'm reminded of Mannerheim's poor Finnish from a book on the Russo-Finnish War I read a long time ago. How long does it take on average for someone learning a very different and grammatically complex language as an adult to be able to speak with few grammatical mistakes? (weasel words "on average" and "few" are deliberate)
With Danish, I'm speaking specifically of stød, which is a suprasegmental unit applied in some contexts in Danish words more or less consistent with
creaky voice. Functionally to an untrained speaker it would sound like a glottal stop, but it's not. It's something wholly unique which doesn't exist in Europe outside of Denmark. And like I said, grammar can be taught. Learning to think in Latin terms where the verb comes at the very end of a sentence, or in German terms where you have to distinguish between locative, ablative, and accusative spatial position, takes some time to wrap your head around, but eventually your mind partitions a space for thinking in those terms. I haven't worked with anything truly weird, but I can understand how an ergative-absolute alignment works. However, with sounds it's different; there comes a point where you
physically lose the ability to distinguish or produce certain sounds, or at least produce them at the level of a native speaker.
As to your second part, I mostly do historical linguistics, so I'm not super familiar with the developmental side, though my girlfriend is, and I'll ask her next time I see her. But like I said, Finnish is really not that weird if we're talking "the full range of what is possible grammatically". To give a quick example: English and Latin have two voice: active and passive, and Greek has a middle voice. Some of the Austronesian languages on the Philippines have up to 5 voices: Agent, Patient, Goal, Locative, and Circumstantial. Ojibwe marks nouns not only for agent-patient, but also in accordance to their relative position on a prescribed hierarchy of nouns. Grammar can get really,
really weird when you start looking outside the traditional Indo-European/Semitic/Finno-Ugric canon.
J/k 
I do this too sometimes, moreso when I was younger... it has always come naturally for me. In my old age I consciously try to resist doing it... sometimes anyway
