..or I could work hard, get my startup to exit, and travel as much as I want for the many years in life afterward. Why does travel have to be done when I'm in my 20s/30s/etc.?
It doesn't, but it depends on what you want out of life. If you want to have a successful business, traveling all the time isn't for you. If you want to see the world though, putting it off until later isn't going to help you any. The longer you put of traveling, the less you'll be able to do, and the more entrenched you will be in your work.
Travel isn't, in my opinion, something you should 'have done', it's something you should be doing. I'm not a big fan of the take a year out, travel the world, then tick it off your list. Travel anything from a week to a month every year until you're too old/sick to get out of bed. My 86 year old grandmother recently flew across the Atlantic to visit family.
The world is not a static place. That thing you really want to see might not exist a few years from now. You can visit the same city a half dozen times and have a half dozen different experiences of the place because the world has changed it between visits. I'd rather take a few long weekends every year than save up for one big trip sometime a decade from now, but that's just me.
Because the human body ages, and traveling involves physical stamina. When I travel, I often end up walking around multiple hours a day for a week or two. This is getting more difficult as I get older. I can imagine that when I am in my 50s or 60s, those tour buses will start looking mighty tempting.