Why do independents choose a party to caucus with?
There's already a question about how an independent Senator chooses which of the two parties to caucus with, but it doesn't address why one would want to do so in the first place.
Based on the current state of the Kansas Senatorial race, there's a definitely possibility that the Senate could split 50 R - 49 D, with Greg Orman from Kansas as an left-leaning independent from a right-leaning state. He has said he would caucus with the majority party, but in the 50-49 scenario whichever party he joins is the majority (51 Republicans with him, or a 50-50 split with him and a Democratic tie-breaker).
In this scenario, I'd think the wise thing to do would be to not officially caucus with either party, instead either voting his conscience (aka what he thinks is best for his state) or bartering his vote on various bills for support for his own agenda.
Is this a realistic option? Is it possible for him to choose not to caucus with either side? Or is there a significant downside to doing so?
While this question addresses just the one Senator in this situation, it could equally apply to two-or-more independents who are close enough philosophically to work together in a closely-split Senate to sway votes one way or the other.