Getting your authority really is the best way to get loads from multiple entities. If you're running for more than one, all the companies are bidding against each other for your vehicle. That doesn't increase your chances of getting the load, only that it will go for a lower rate. If you have your authority and you're the only van in a particular city, you know you're going to get the load and you're going to get more money because of the lack of competition. If you're the only van in town and you're signed on with three companies, each company might have you listed on the alliance and each company is going to look on there, see two other vans posted, and bid accordingly. Your carrier can get more money for a load if they know there's no competition, which could mean more money in your pocket.
Now you might say that you're on a contract rate so you don't care what the carrier gets, but why do you think driver pay is where it is and how much more would it be if carriers were getting better rates? This is a supply and demand business and if there is a perception that the supply is at a certain level, that is going to directly affect rates. We make so many decisions based on what the competition is in a certain area: how much we bid on a load, whether or not we suggest a relocation for a certain unit, etc. The other day I was looking at the number of vans posted in a certain area. There were 20 listed and I was about to tell the driver to relocate when he told me that there were only two other vans parked where he was. When I looked carefully and started eliminating the ones that had the same specs as another vehicle that I figured were listed by more than one company, what appeared to be 20 vans was whittled down to 9. It's really pretty simple to figure out. More companies bidding=lower rates.