As I said, to keep an eye on what is going on inside the NW. The Raven is always with Mormont, thus BR knows everything that goes on in Mormonts private councils
Why would he need contact? He can just reach out with his warg skills and take over. I think there's also a reference to the bird being old, or being around a long time, possibly even from BR's time in the NW, although I admit that is a reach.
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The Mormonts may be wargs, or at the least have greendreams, but answer me this - Why would Mormont warg the Raven when he is being attacked by a wight so the raven can shout "FIRE! BURN!" when he can just go "Jon, burn it!"
Why does he want Bran? Yes, for his power, but
why does he need Bran's power? To fight what is in the north of the Lands of Always Winter, because that is when the 3EC tells Bran
now you know why you must live. The obvious answer is to defeat The Great Other, and that is what BR, the COTF are working towards (unless you go for a crackpot contrary theory

) Bran was marked out 200 years before he was born as a great and powerful warg, its pretty obvious (to me anyway) that BR is training Bran up to be his replacement - the dude is 150 years old and he pretty much admits he ain't got long left.
The motive is, as above, to help the NW defeat The Others. And as I said above, how else, or how better, could BR keep an eye on the NW than having his own eyes and ears with Mormont at all times?
But to turn your own questions back on you, what is Mormonts gain in having a raven he could warg, except it never leaves his side?