Blue Lanterns and green lanterns

when blue lanterns are near green lanters how do they become more powerful than the other lanterns

BL's are powered by Hope and in the concept of being against insurmountable odds most people would lose the will to fight with no will to fight the insurmountable odds it basically acknowledges that those who give up believe there to be no hope left. However if one person has the will to go on you know that person has Hope that he can either win or make enough of a difference.

The more will a person has to accomplish their goal the more hope that person would have of succeeding. Though things like Rage can be a motivator some people who choose to follow Rage can fall under the concept that they believe they have no hope of winning but they'd rather die fighting.

Blue Lanterns are generally seen as the most powerful, but also the weakest of the Lantern Corp. Hope is nothing without the willpower to do something about it, so the absence of a Green Lantern means that a Blue Lantern can't really do anything much beyond fly and breathe in space.

With a Green Lantern nearby (which can be quite a distance, considering most things) a Blue Lantern is capable of amazing feats. They can nullify a Yellow Ring and destroy a Red Ring. In the comics, with Hal Jordan on a nearby planet, two Blue Lanterns stopped a sun from exploding by reversing its ageing process by several billion years.

While Hal was still in possession of a Green Ring, those two same Blue Lanterns took on the majority of the Sinestro and Red Lantern corp combined (that is, if I remember correctly) and were pretty much winning until Hal had his ring nulled by Atrocitous.

All things considered, wouldn't it make sense for a Blue and Green Lantern to team up on a permanent basis?

I think there should be a Blue Lantern assigned to each sector of space to help the Green Lanterns but it takes so long for Blue Lanterns to be chosen it will take a long time. Plus the Guardians have become jerks lately so they probably don't want their Green Lanterns teaming up with any other Corps.