I'm not about to have a lawn in part of the house, or paving slabs, or a lupin bed to chase each other round and through, or birds to be ambushed from it, or bushes to sunbathe under, or birds flying around inside for them to watch. My back garden, which they cannot get out of, provides things I cannot or will not provide indoors. It makes their environment richer. They like it enough to go out in quite damp conditions, and to demand to be let out several times a day - they don't have free access at present as I have two kittens I'm not letting out just yet. Normally they come and go as they please.Amen to that! I will never understand why people think cats need to go outside just to have fun because there are many toys, condos, towers, scratching posts, window perches, and cat food dispensers to choose from and other items for training cats to stop destructive behavior. If the cat goes outside alone, it is not with its guardian, so keeping it in strengthens the human/animal bond if you teach it to love staying inside.
Are they bonded with me? Well their choice is to sleep with me, on or in the bed, almost every night. They come when I call, and will make it quite clear when they want to sit on my lap and be petted. To me that's pretty good bonding.