I wonder how well the removal of certain noises will be. I've done some pretty basic audio editing with Audacity, and it seems like systems designed to remove certain sounds is still tricky. There's an effect that can be used to remove a certain sound, but you have to have that sound isolated - and it's still doesn't always work 100% (For example, keyboard clicks are almost impossible to get out, in my experience). It seems like with noise removal, it's not always easy to get just that sound removed; you usually either get to remove that sound and a bit off of others, or get to remove most of that sound. On top of that, it would be tricky to, say, have a program that could remove a chosen sound, like rain or a baby crying, from a drop-down, because they will deviate from a standard preset due to things like pitch and what's between you and the source of that sound (rain on a metal roof sound different from rain on a wooden roof). That would mean, for a lot of cases, you would have to choose the sound manually, and make the app ignore that sound. That means you would have to use something similar to the Noise Removal effect in Audacity where, if you don't get just the sound you want to remove, you end up with everything being slightly distorted.
I'd be perfectly happy just with something as simple as a low-pass filter. That would take care of sirens, babies crying on planes, cats yowling at night. It wouldn't help with the rain-on-a-metal-roof, but I'm not sure I'd want to silence that - it's the cosiest sound EVER :)
I love the sound of rain, too. So much, in fact, that I have an alarm clock that makes that sound when I go to sleep (and it's hard for me to sleep without it!). However, I've met people that have trouble sleeping when it rains. At the same time, it seems like a filter would either not completely remove intended sounds, or remove it and most of all the other sounds. I hope they got some magic, though.