... how pervasive the new Global Language already is ...
I'm going to challenge you on this point. First of all, what's Chinese? I'm guessing you refer to Putonghua aka Mandarin, the erstwhile variant of Beijingnese prescribed for official use within the PRC by their political leadership.
And second, how "global" is it? It's useful primarily in one contiguous area of the world. Even there a large chunk of people kind of learn it as a first semi-foreign language because they speak something different at home. Cantonese, Shanghainese, or a language that cannot be written in Chinese characters.
Which brings me to my third point: a language that requires study of a script this idiosyncratic will not rise to a global language. Vietnam has gotten rid of hanzi, Korean pretty much as well. Ironically, the north has already completely abandoned it. By comparison, the Latin alphabet was spread by cavalry and cannon boat into all parts of the world for centuries. It spread so far that it is now used to teach pinyin to PRC schoolchildren. And while it is not without its own problems, the simplicity and adaptability of this phonetic alphabet to any language makes it far more useful than Chinese characters. And I'm not shitting on the cultural value of them: that's unimpeachable. It's just too complicated.
The alphabet spread with English, Spanish, French, and Portuguese all over the world. I'm not saying that's a good thing but it's already happened. Mandarin cannot have a similar success today unless the PRC starts colonizing at gunpoint fast.
Most Chinese as a foreign language speakers outside the PRC learned it for economic reasons. Economic ties have become somewhat dicey. If anything I suspect interest in learning Mandarin to wane.
There is also the tonal aspect. Any atonal-native language learner is going to have a much harder time than trying to remember the non-sensical English orthography.
More people on this planet learn English as their first and possibly only foreign language - if they learn one at all. The forum you asked this question on is in English. The internet cements the use of the alphabet.
I'm in Japan where foreign language education is notoriously sub-par overall. English is the first foreign language. Some private high schools offer Mandarin as an optional, I haven't seen anything substantial in state-run schools. At college level, most people chose between French and German as a second foreign language. Like we're still in the Meiji Era. I'm a big proponent that they abandon this tradition in favor of Russian, Korean, and Mandarin. It always helps to learn the language of your neighbors. Language schools advertize k-pop-trendy Korean more.