One comment regarding Wikipedia: you may be aware of the “Simple English” language option, which can help with making some pages more accessible. It’s in the language menu, or you can just change the language prefix in the URL, such that your example above becomes https://simple.m.wikipedia.org/wiki/Taylor_series. Granted, it’s not immediately obvious that it’s there, but perhaps it’s one reason that the main article can be more precise off the bat rather than explanatory. Furthermore, I wonder if Wikipedia math editors are less concerned with the notion of an encyclopedia as learning device and treat an article as a canonical overview of a topic, with all of the baggage that comes with that.