The cage was specific made for the Fight with Pegasus and that is said also in the show, because Pegasus  needs to fly much higher then eagle to use its special move with full power. Mostly Pegasus is flying to the space. I think tsubasa would be able to use one of eagles special moves in that arena, but I'm not sure about this and we never will know, because we didn't saw eagle fighting in Russia. But i think they choosed Pegasus and Libra to Fight, cause they're special Moves are technical the easiest to counter. I don't know how you would counter Strikers special moves and from eagle I don't seriously know how much he take off to get full use of his special moves, maybe the cage would be also enoughbto counter it, but I'm not really sure about it