Question: value of phragmites?

Phragmites (Common Reed) - Often a damaging, invasive weed in Ohio marshes, but potentially also a food source for some wintering birds

December 24: Today I was reminded of a question that first occurred to me a couple of years ago.  I was birding along the edge of a marsh north of Oak Harbor, and I flushed a flock of about 30 American Tree Sparrows from a big patch of phragmites.  I've found flocks of these sparrows in this habitat before; are they mainly using it for cover, or are they actively feeding on the phragmites seeds?  

Phragmites australis itself is a problematic plant.  The species is native to North America, but in recent decades it has become dangerously invasive in many regions.  Here in northern Ohio, marshes that used to be varied and full of life have turned into solid stands of phragmites, crowding out other plants and supporting relatively little wildlife.  Research has shown that the invasive phragmites is actually an alien strain, introduced here from other continents.  Managers of some wildlife areas in Ohio have gone to great effort and expense to control phragmites, to maintain some room for other species.  

Of course, some species of birds will find a way to take advantage of almost any plant.  Tall, dense stands of phragmites provide a certain amount of shelter for birds in winter.  I've often found flocks of American Tree Sparrows in such places.  Once when I had time to watch such a flock for a while, I saw that the birds were actually perching on the tops of the swaying stalks and evidently feeding on the seeds of the phragmites.  Today I watched the birds to see if they would do the same thing, but apparently I had approached them too closely; they would not go back to feeding while I watched, and eventually they flew farther away to an area where I could not follow.  So this will be a question for future observation.  American Tree Sparrows are very common near Lake Erie in northern Ohio in winter; how important are the stands of phragmites as a food source for them?