Well, modifications to Mercator world maps are not a bad idea, people genuinely don't understand the size differentness (both ways - equatorial ppl how smol northern & southern territories are & the other way around, eg Europeans how big most of Africa is in comparison).

The bad part of normalising anther type of sphere projection for this purpose is that it almost certainly wouldn't follow just one simple rule like Mercator's. And with that exact predictability actually diminished in a way.

Eg, we could try to keep countries as close to the same-ish size & in return shrink (or have gaps in) oceans. Or keep smaller gaps between counties/some squares. Or have several different projections merged into one global map. Etc.
All of it is always arbitrary.
The true answer is only education (not necessarily, but preferability in early school days).

wiki/Waterman_butterfly_projection:

If they're really concerned with how big they look on a map, they should advocate for the Madagascator projection.

Every single 2D projection of a 3D spheroid will be trash. All of them.

The only difference is what you're going to distort.

...I should feel more invested on that, given I'm from SA, but I don't care too much.

Mercator is a good projection for navigation for a variety of reasons. It should never have been used for geology classes in schools, but I think what originally happened is schools would just buy a nautical chart and put it on the wall.

Even when I was at school long before that episode of West Wing, my classroom had a Robinson Projection map, so the whole controversy seems like something that was ginned up possibly decades after Mercator was no longer in use except where it's needed.

That being said Google used a broken version of mercator on their maps for many years..

I vote for the Waterman Butterfly Projection

why are we changing maps ?