Very true. But that's partly the reason they call organisms such as peas (or mice, or worms, etc.) "model organisms", cos they lend themselves to easy study. Peas for instance grow fast and produce prodigious progeny compared to most other plants, they're hard to accidentally cross-pollinate with neighbors or wild varieties, etc.

In this respect he wasn't so much lucky, as he chose wisely. And he chose the most virile phenotypes (after experimentation), rejecting many others. It's in choosing the specific phenotypes that all resided on different chromosomes that makes him lucky, though as statisticians say his results also were lucky to show so much consistency.