One time, I received an offer from a small, struggling startup. But because it's equity structure was so simple (struggling has a way of simplifying things), I counter-proposed taking less salary for more equity, and they agreed.
With the typical equity opacity removed, I viewed the trade-off as more of a bet on myself: the impact that I could make and if I assessed the company correctly.
The payoff when we were acquired was just the equivalent of a nice extra bonus. The real satisfaction was having more skin in the game, having the expected impact, being correct on the assessment, etc.
But it wouldn't have happened if I felt lost in the complex equity structure and confidentiality barriers that seem to be present in many startups.