Which would be the principle application of a global simulator.
You're completely wrong.
The simulation of every speculative scenario.

Example:
The world is changing due to human error (massive impact on the sensitive adjusting screws of nature). What could the future look like? Our ...

Hopefully the seams can be situated in non-critical areas where a little distortion can be tolerated.
There are no non-critical areas in global simulations of any planet.
Noticeable inaccuracies due to distortion already occur to a greater or lesser extent in Canada and Scandinavia in almost all ...

I thought that spherical maps were called globes . . .

Global projection, to put it aptly. The topic is still a hot potato. So far nobody has succeeded in presenting a practicable two-dimensional representation of the world as a general-purpose world map that is conformal, equidistant, equal-area ...

Sinusoidal maps are equal-area - critical that the hexes all be the same size.
Correct, but on Sinusoidal maps the polar regions are heavily distorted. Sinusoidal Interrupted significantly improves this shortcoming. However, a seamless hex mesh at the seams of the gores is impossible, which is ...

Why use hexes at all? Why not just use a google earth 3d type of map and real distances?

Does not work with board games and board game simulations such as Civilization & Co.

I mentioned GDW's 1981 award-winning sci-fi game Invasion: Earth, set in their Traveller future history.
Marc Miller, Frank Chadwick & team didn't know any better back then. HEALpix had not yet been born. Today, the world map and Traveller templates would be based on HEALpix. Maybe Marc will ...

I would have more hope for a sinusoidal projection:

https://up.picr.de/48874585ms.png
Sinusoidal Inerrupted would be the very best solution. The more gores, the lower the distortion. Compare this with Tissot's indicatrix.
However, this projection method is not suitable for hexagons ...

I am not sure what you mean by that? Where have you seen this claim?

All attempts to generate worlds without pentagons have failed miserably (see Civilization & co.)
This wisdom comes from several developer forums.

https://up.picr.de/48872195yx.png

Say goodbye to the icosahedron. The ideal projection of a world map consists of an inflated six-sided cylinder with a lid at the north and south poles (hexball projection). The cylinder is rolled up and the poles at the 54th and -54th latitude are unfolded ...