There seems to be very little ways to get rid of supports.

Am I missing something there?

I know they sometimes have higher cost.

But even a support like speeder bike will be there round after round adding to your die pool.

Seems like a huge benefit to really stress having a few supports in your deck.

They're not very action-efficient, since you activate them to roll only a single die. Also, 3 resources for the bike is a hefty price when you only get 2 a turn, and if you want to play even a single die negation effect that's likely half of your allotment. Not to say supports aren't going to be a good choice in a resource heavy deck, they just don't have the ease of use that upgrades do.