Shouldn't "reaping the rewards" include seeing your equity/shares
become much more valuable? If so, should one join a start-up only when
equity is written in the contract?
If your only goal is reaping rewards, then you probably should avoid startups - without regard to the equity being offered. I worked at a several startups, most of which never paid significant financial rewards. If you are talented, you may be able to accrue far more predictable rewards at a larger company.
That said, I would never trade my years at startups for big-company jobs. I was able to learn things far more rapidly, to advance very quickly, to work with extremely smart people, and to feel that my efforts made a difference - far more often than I ever did in larger corporations.
At startups my years, my contacts, my learnings, my professional network - all of these were valuable to me in ways that never happened at big companies. At several startups I got to do things I never imagined I would have a chance to try, and I never imagined I was capable of. For me, the hard work at startups never seemed like a burden, and always made the work day fly by.
If you want to work at a startup, everything else being equal, then an equity position can give you a possibility of a bigger reward. But remember, it's only a possibility. Startups are often shooting stars - burning brightly but often very briefly. There's no guarantee you will be in for a significant reward (if any).