And that’s the tradeoff of using a globe, whereas the tradeoff of the Peters projection is that the map is distorted in various ways, and the tradeoff of Mercator is that the map is distorted in other ways.
Which is why that West Wing clip is, frankly, pretentious, because it doesn’t discuss the negatives of Peters, wrongly implies that it’s “the” correct way to view the world, and makes no mention of other major projections, or even a globe.
Choice of map projection is all about context. Peters is sensible in a particular context; Mercator in another; a globe in another. My usual projection of choice is Albers, which is typically great for the continental US, but I probably wouldn’t use it so much if I regularly made maps of other places!
To be fair, the West Wing was pretentious in so many other ways that this is one of the few clips that borders on genuinely educational. Flawed? Yes. But it's not an educational show, it's a bizarre hyper-liberal hour-long lecture to the viewer where for some reason every single character talks like an over the hill Jewish man with the same verbal tics and expressions.
And honestly, it's a bit pretentious to publicly denounce an entertaining TV show just to seem smarter than everyone at cocktail parties.
It's crazy how populists and misinformation agents have successfully convinced people that any mention of a potential bias is an "woke" attack on their whole personality and world view.
Only if you count bad evangelists as "misinformation agents". There are unfortunately plenty of bad actors who have persistently tried to use it as a social cudgel and an excuse to fight for social dominance, shield oneself from being questioned (including self-reflection), and to write others off. To be frank, it is no wonder people view it as an attack when that is exactly what it has been used for.
For a similar patterns of bad behavior by the same actors look at the utterly terrible framing and naming of white priveledge, where not having problems nobody should have to deal with is phrased as if not being discriminated against is a moral problem!
With a globe you can only see part of Earth at once.