Is it normal my rabbit loves his cage

My rabbit prefers being in his cage. I have set up a small play pen outside it and the door to his cage is always open (except at night) but he stays in the cage. I also take him out several hours a day, let him free roam in the kitchen where there's almost no wires or other dangers on the floor, but he doesn't run around much and looks a little stressed and often goes up to the gate wanting to get past it to go back to my room where the cage is.
He is not depressed. In fact he looks and acts happy. He always comes and licks my hand when I come up to him and he throws himself down on the side while in the cage which rabbits do when they feel happy and safe. He eats and drinks well. The breeder also told me he's a calm personality and he certainly is calm except when he's chasing our cat around lol! He doesn't even mind being held, he licks me a lot when I hold him and enjoys getting pet so much that everytime I sit next to him now he puts his head down expecting me to scratch his head and neck and then he bops my hand with his head and licks it. So is it normal for a rabbit to be happy in his cage??? I feel a little bad and worried for him but maybe he's similar to me who enjoys sitting in my room lol! Should I make him leave the cage more? Is it bad for his health and mind to stay in there? Anyone here knows rabbits well? And is it normal for him to sleep a lot? He's either sitting eating hay for hours or sleeping it seems, though occasionally he just starts jumping around in and out of the cage like crazy!