Tools like this one might be better at highlighting the flaws of map projections, but I don't see how anything could be better than a globe at showing the true relative sizes and shapes of countries, since it shows them as they actually are. In what way do you feel the globe doesn't show the differences between countries well?

In what way does a globe not do a good job showing the true size of countries?

The biggest problem with a globe is that it is round.

In this case, that means you can’t see all of it at once, which means you’re relying on your visual memory unless you actually pull out calipers.

Seems like this could be easily fixed. Make the countries on the globe removable (magnetic?). Then they could be moved over other countries to get a direct relative comparison in the same field of view. Similar to what the OP web site is enabling.

Or have a conventional printed globe but that has a clear "shell" with an engraved map that can be freely positioned to overlay any part of the "shell map" atop any part of the conventional globe surface.

I have no idea how the mechanism allowing this globe within a globe would work.

As flexible screens get better maybe a globe whose entire surface is a touch-sensitive display that allows gesture control of the map content?

A possible issue with this is that due to the spacing between the two concentric globes the countries on the external one will appear bigger than the ones on the internal one.

Perhaps the engraving on the outer shell would need to be done on the inner surface?

> Make the countries on the globe removable (magnetic?

Countries as jigsaw puzzles pieces, made with soft Silicone, should work as well