> However, the irregular tiles actually bother more than if it was a standard geodesic sphere which only had 12 pentagons. For one, the fact that tiles are different sizes looks kind of weird. More importantly, this tile layout could actually make an important strategic difference (much more than if there were only 12 pentagonal tiles). Assuming movement costs between adjacent cells are constant, a straight line may not be the fastest way between points anymore! Looking at the heavily distorted mesh example, I can see several places where a path through a few large cells has the same movement cost as the straightest path.

I would say there is nothing wrong with strategic differences, so long as they are irregularly distributed. Regular or predictable distribution would cause strategic ruts. Also, irregular movement costs are a feature. Ancient spice trading routes and deer paths in the woods rarely follow straight lines either.