Yes the bow hunt is more than just the opportunity to take possession of an animal to me.
I've been at this 47 years now. But I remember a span of time in my 12th and 13th year (80-81) where I was hunting for giant deer on a large property that had them. It was northern Indiana (Elkhart) and in those days a bowhunter was allowed only one deer. The bowhunter was not allowed to hunt with a bow during the gun season.
In those two years I kept a diary. I passed on 110 bow range shots (20 yards or less). I never shot an arrow during those 2 years. Yep, the trees were beautiful, fresh air great, anticipation super high, and lots of other wildlife entertained me. But....
Towards the end of that 2 years I realized I was loosing the excitement for seeing ordinary deer. When I saw a deer and knew I wasn't going to be tempted to shoot, the rush didn't occur.
I realized that because there was going to be no moment of truth, no risk that I might miss or worse, that my hunt was missing something. It became exactly like hunting with a camera for me (with no market for a great picture there was nothing at stake ruining a picture).
I had turned hunting into something else.
That 2nd year I was hunting for a small buck with a muzzleloader on that property. The largest live deer I've ever seen (12-point) walked within 15 yards in a picked bean field to the pin oak I was perched in. I lowered the sights on him and decided I didn't want the biggest deer of my life to be with a firearm. That big ole buck hung around with a doe for more than 10 minutes. I moved those iron sights from his neck to between his eyes. I had decided, since this spot was adjacent to a near implantable button bush swamp that I was going to drop whatever I shot in his tracks (I didn't bow hunt next to this marsh). I passed the deer. No regrets and I never saw (that I know of) that deer again.
I shot a little 6-point, between the eyes at 35 yards that evening with that .50 caliber Renegade. The only step he took was down.
So, I enjoy a walk or sit in the woods more than most, but if I don't have an unfilled tag in my pocket and the intent to fill it, it isn't a hunt for me. I'm not bloodthirsty, but I thrive on the last piece of the complicated and beautiful puzzle being completed.