In only one of my games did a minor became the dominant power. But since they were fundamentalists, I guess it's an exception.
On the other games, by the time I catch up the AI (in population, & research) I have to help the minors stay alive against AI attacks, so that I can transfer my trade routes to them, when they become available because I attack some other AI.
Then if the minor is really getting crushed, when they have only 1 or 2 ships left on their planet, I invaded, just prior to the AI invasion: in order to save them, I had to take them

.
And I agree with Lord Megatron, there should be more of them. Carinoids and Alexians can defend themselves for a while, but the ones that appear mid-game, with a tiny 100 people in the planet and no ship to defend it, are just taken out as they appear. There isn't even a fight: it looks like my invasion fleet just landed on their base camp by mistake (crushing it, but it was not even in porpuse...), and then occupied the planet!