Agreed, the rescues I work with don't adopt until at least 8 weeks. For starters, you don't know that your adult cat will "accept" the kitten. You can't just put them both in the same room and expect it to work out. I recently adopted a 5 month old kitten, and it took about 3 - 4 weeks of keeping her in a separate room, letting my other cats smell her, letting them see her, then gradually introducing her in small increments. It can be quite time consuming, but the slower the better.
And as others have mentioned, 4 week old kittens need a LOT of care and attention. They need to eat every couple of hours (and they cannot eat dry food). And they can get sick very quickly, so it's really not a good idea to leave them unattended for several hours.