There were many years when my commute was fifty miles round trip. For most of those years, I rode to work five to seven days per week. For a couple of those years, my wife and I were both also in grad. school; she was also working full time. Fortunately, shortly after our son was born I was able to transfer locations and have a much shorter commute. We would have needed to use some sort of day-care or hire someone to do the house remodel we were doing in our spare time if I had continued with the prior commute.

So, I guess I can say that a slightly less than sixty mile r/t commute leaves plenty of time for other interests. I think the reason your time analysis indicates otherwise is two-fold:
1. It won't take you five hours to ride sixty miles if you put some effort into getting faster.
2. Assuming you desire to live a full and healthy life, you are going to need at least an hour per day of exercise anyway. Now you can get something else done while getting that daily maintenance done. For me, time in a car is time lost. Time on a bike is time enjoyed.

If you are committed to riding slowly and you don't feel any need to stay healthy, then commuting 300 miles per week will feel like drudgery. If you enjoy the ride and can get your speed up, it will leave you feeling energized and leave you plenty of time for other pursuits. However, we all get 168 hours per week and no one can really assess how best to allocate those hours other than the person who is living with the decisions.