You hit it on the head with "irrational [sic] optimists" even though you whiffed it with "typically worthless."
There are at least two very much rational psychological pieces at work here. The first is that people who are inclined to be optimistic about a tiny stake are qualitatively different. The second is that the stake's expected value (EV; probability * outcome) is not a sufficient metric upon which to estimate its utility to actual humans.
1. People who are, relative to a theoretically precise EV, optimistic about a tiny stake act qualitatively differently toward the organization than those who are neutral or pessimistic / jaded.
For example, a good friend of mine in school used to argue, "why vote? one vote can't ever move the needle." And he was, after a fashion, right: the expected value of your single vote in terms of affecting the outcome is nil. But if you were looking to build an organization of people to achieve some political or social outcome, you would ceteris paribus want those who DO vote despite that expectation; voting here is a proxy for caring, motivation, social cohesion, deontological orientation, etc., not as the jaded comments here might suggest by analogy, mere innumeracy.
Similarly, and I want to take care to say that I hold this position only toward the case of creating high-growth uncertain ventures (startups) and not as a general prescription for society or the economy, those who eagerly accept and seek even a small ownership stake in the enterprise are going to be qualitatively different. And you may very much want that, just as they want to be part of something they have some ownership in.
2. Convexity and utility functions. Get over the idea that a dollar is worth a dollar. The first dollar to the guy who needs that dollar for a bus ride home in the rain is worth more than the 1001st dollar to a similarly situated guy -- an easy proof of non-constant marginal utility. But if you look into things like indivisibility and status tournaments, there's lots of good research that points out that playing the lottery can be rational even with a negative expectation under certain utility functions.
In other words, a 5% cash raise, to a comfortable software dev whose needs and retirement at a middle-class level are nearly certain, may be less desirable than a smaller EV shot at a life-changing sum. It may well be worth $10k to buy a "lottery ticket" at a one-in-two-thousand chance of a $10 M outcome ($5k EV).