Passenger pigeons were not primarily a grain species, although they would eat grain when other preferred foods were in short supply. Part of the reasons the flocks increasingly turned to grain with time is due to the cutting and burning of many of their native forests to make room for farmland (and with an average lifespan in captivity of 15 years, probably half that in the wild, populations don't readjust right away). They were a migratory species, of course, but the habitat destruction was going on all over their range. If you get rid of the oaks and chestnuts in an area and the only other food option is grain, of course they're going to eat that. They also ate insects, mainly when breeding.
When you're talking about reintroducing a species from scratch, obviously the issues of what to do if a billion birds come into the area is totally inapplicable. The forests capable of supporting those numbers are gone. Birds that primarily consume seeds and grains are a much bigger threat to farmers than birds with a primary focus on nuts like the passenger pigeon.