Are your sunflowers being stripped? Are the leaves acquiring non-snail-like holes and then disappearing altogether? You may be feeding the birds, but not with the seeds!
Lesser goldfinches apparently are nuts over sunflower leaves. They will tear little bits of the leaves off and injest them, and within a day or so there will be nothing but a stem and a flower.
If your goal is to feed the birds, then this is okay. If you have bird problems on your vegetables such as peppers, then you may want to plant sunflowers off to the side to distract them.
Why do they eat sunflower leaves? They must like a little salad with their seeds, and sunflowers are particularly yummy for them. In searching the Internet for suggestions as to why they like sunflower leaves so much, there were many postings about the incidents, and yet most respondents insisted that the birds were after bugs on the leaves, or that snails came in the night and ate the leaves!
This occurrence seems to happen mostly in California, and other than bird nets (which one person said that the lesser goldfinches chewed through!) or planting sunflowers thickly (one for them, one for you), you may as well just enjoy the show. Ours come up from dropped or buried birdseed, and when the plants are growing their flowers, suddenly they are beset by birds who skeletonize the plant. We’re okay with that; it saves a little cost on the very expensive Niger thistle seed! (Oh, and by the way, Niger thistle isn’t thistle seed at all).