Cycling is about 40 minutes both ways. I take it a little easier on the way to work because I don't want to sweat too much, and then change in to my work clothes and do a hobo shower in the single stall bathroom. On the way home I can choose my pace, unlike when I'm driving. I can mash the pedals and let off some steam when I need to, or I can mosey home when I'm getting burned out. Stopping along the way is much easier. I'll grab coffee, or a snack, or check out a used book store I've never seen before. Plus, you are much more a part of the world when you are cycling, and you can look around more and notice things you wouldn't when driving. I'm sure a lot of these things hold true for motorcycling as well.
I'm not much of a morning person, but I find it much easier to concentrate when I arrive at work after cycling in. I also find myself much more energized when I get home, even if I'm pretty tired when I leave work. I find taking public transportation provides some of the meditative aspects, since I can reflect on my day more when I'm not driving in Chicago traffic, but bicycling allows me to combine my commute with exercise, which is amazing from both a mental health and physical health perspective.
That being said, riding a bicycle is certainly more dangerous than driving or taking public transportation. While I can take steps to mitigate the risk, I need to cross a number of bridges and go under a number of viaducts on my way to work, and the risk is substantially higher while on a bike than in a car, bus or train. I don't think I'd be comfortable riding my bike on my current commute if I had a kid.
But to the primary point, I also thoroughly agree that downtime is important, and there's a danger of trying to optimise every waking hour too much. Learning the art of structured procrastination (neither too much nor too little) should be part of every pragmatic programmer's toolkit.