I think that kites have been getting a lot more "help" than other birds, what with them being pretty easy to reintroduce, and being a good poster child for conservation efforts. It's very obvious to see the effects of the work that's been done since there's a big difference between a handful of pairs in Wales and the much larger numbers we see now, so they tend to get prioritised. No one will notice if we have a thousand more sparrows, but a thousand more kites can't be overlooked, so that's where the money goes.
(It's a bit like how we'll donate money to save pandas or tigers but no one cares about all the insect species that go extinct.)
Many bird species are in decline whether there's kites in the area or not. So bird numbers are down for many reasons, but kites have been getting a big helping hand and sparrows and starlings haven't. It's easy to think that kites are the problem, but the problems with songbird numbers go much further back than the reintroduction of red kites.