Examples: if I didn't happen to have an accurate-enough figure for the diameter of the Earth in miles, plus a formula for the surface area of a sphere, plus roughly the proportion of the Earth's surface that's land, all in my head, there's no chance at all I could produce a useful-for-any-purpose-whatsoever estimate of "area of the Asian continent" without researching it (at which point I could just look up a fairly exact figure, without knowing any of that). Year of Alexander the Great's birth, well I happen to know roughly when Aristotle was active and that they were alive at the same time. Otherwise, again, I'd produce a useless-for-most-any-purpose guess. Total US currency, I bet knowing something like the current annual GDP of the US would at least narrow that down, and is something someone might plausibly have at hand (I don't, my guessed range on that would be hilariously bad). If you have a sense of blockbuster movie budgets and/or returns, which one can acquire from paying attention to entertainment headlines, it's easy to come up with a reasonable range for Titanic's box office receipts. And so on.
Is the point that trivia's highly valuable, actually, if you have to estimate a bunch of arbitrary stuff purely from memory?