The point of not allowing Summons is because Tournaments are supposed to be about YOUR strength over everyone else, not about what Corp youre in or what summon you have.
Summons = a Familiar, meaning another entity fighting alongside you... that doesnt sound like youre fighting with all YOUR strength now does it.
Thats the same reason why we dont allow Pill's, Oil's, or Corp Items. (Nb4 people say it, nah Swords and weapons are supposed to be an extension of YOUR body.)
I dont mind Making a "no bars" style Tournament where all of this is allowed but i guarantee a majority of those who participate will complain.