I recently got a new kitten and we decided it'll be an indoor cat (though I'm harness training her so she can go out on walks). I've had several cats over the years die because they were allowed outside (one got hit by a car and one I think got locked in my neighbor's crawlspace/basement though we never found her). I personally haven't had many of my outdoor cats bring me birds, but where I live now we have bird feeders and don't want the birds preyed on.

Edit: I forgot about the outdoor cat I had that I left at home when I went off to college. It got run over by my neighbor because it was sleeping under his wheel and he didn't notice.