adzling, if a mage has multiple spirits at their disposal on a run, then they are most certainly using Binding, and paying for that privilege, both in nuyen and the resources dropped on getting the skill. If they're dropping edge, they're spending that, too, and won't have it available when they are on the run. You can only have one summoned spirit at a time.
As for the 'spirit army' there ARE characters that do that in the lore, actually. Man-of-Many-Names, Elijah, and Serrin all qualify. However, they are very much loners, and this is a 'team' game, so that might be a problem for some groups, I understand.
What you do in that case is take the player aside, and have a friendly chat about not going overboard with things and ruining the fun for the rest of the group. If they ignore this, then you repeat the friendly chat after someone geeks the mage first, for reference on their new character. As with most of the things, there is only a problem if the GM is asleep at the switch.