Grammatical complexity, in my opinion is overhyped as a barrier to language learning. In my own experience, after enough time and pratice you eventually internalize grammar structures without a problem. The real issue is learning enough vocabularly to express yourself not simply fluently, but eloquently, and to be able to make it through any text you find.
Also, a few problems in your argument against Mandarin: tone really isn't a barrier. The writing system, which is not an alphabet, would actually present difficulties, but I wouldn't consider it an intrinsic part of the language - it could be changed. Writing English isn't much better, but similar complaints could be made for French.
(It should be noted that Manadarin morphology, on the otherhand, seems to discourage borrowing words, and most things are imported as calques. This could be viewed as a either good thing or a bad thing.)
Languages, in general, are around the same level of complexity. We can make comparisons and say that English inflection is massively simpler than Hungarian's , but we shouldn't concluded based on that assessment that English is simpler than Hungarian, but that this complexity is simply distributed differently.
English has a lot of relative benefits: it's closely related to a lot of widely spoken languages. And a lot of people speak it. It's not even close, even as a speaker of Spanish, which has more native speakers than English, it feels like a Sisphysian effort to find content that's just as high quality as I have been accostumed to in English, and inn any type of quantity. But none of these advantages are intrinsic to English.
My central thesis, after all, isn't that Mandarin or Hungarian, or even as easy to learn for most of the (IE speaking) world. It's that the supposed advantages of English aren't its grammar, and that English isn't a superior language by any means. History, not lingusitics, has allowed English to enjoy as much widespread diffusion and prestige as it does today.