With their constant invasions and refusal to leave new colonists alone, current League feels more like a more evil Hegemony competitor or organized and ruthless criminal or pirate organization. The lore may say that they unite against Hegemony, but in practice, they are a higher grade of pirate that does not tolerate new colonies.
League and Diktat feel too similar now, mostly in what they use. Lore may be subtly different, but that does not matter compared to what they use.
Hegemony does not attack colonists simply because player colony put up Tech Mining or just grew too big. They bully player for other reasons if seen.
Tri-Tachyon is about as impotent as the Luddic Church, although they are great to rob blueprints from. Luddic Church has no heavy industry, and thus has weak fleets and nothing good to rob from.
As for what faction the game lacks? A significant take-no-prisoners enemy-of-humanity faction. Remnants are probably it, but they are not aggressive. They only appear when player is deliberately looking for them (or does the two unique bar missions).