Problem is if the OTHER player doesn't download the skin or decides to screw around and replace certain skins with other ones, you won't show up in what you THINK you show up as.
It's the way it is now so that everybody sees the same skin.
Think of Counter-Strike. There are low-res models available that make CTs a bright blue block and Ts a bright red block. Makes it easier to see.
Well what if they made all perk planes bright pink (the better to track them with?) or screwed around with subvariants (a white 109 is an E, a red 109 is a G, a blue 109 is a G6, etc etc) to sort of "cheat" and help themselves figure out what planes are what before the icons kick in.