Wow, that's incredible! I didn't think a rooster would do something like that.
I did hear a similar story about wild birds though. There was a pair of blue birds that had eggs, but the mom was killed. So, the dad sat on the eggs, hatched them, and successfully raised all the chicks by himself.
Wild birds often take turns on the nest. One will sit while the other feeds. Blue birds will even take turn feeding the chicks once hatched. Tufted titmouse are the same. We have bird houses around the property and those 2 breeds are the majority I've sit outside my shop watching.