[@Raineh Daze]

Perseus can't use Pegasus properly anyway Rider or not, he's not a very good 'pure' Rider. 

That being said I presume he has a means to summon Pegasus using magecraft under Rider just like Medusa does.

Bellerophon is pretty useful even without Riding, but it really doesn't have a place out of Rider. It thematically doesn't work I think.