I dislike the idea of making cult troops elite-only. Making defensive ground-holders like Plague marines elite who can't hold any objectives at all defeats their purpose.
I actually like what they did in the recent DE codex: troop and elite version of the same unit. Want affordable CC specialists for a decent price? Get vanilla troop Berserkers. Have more points to spare for pure slaughter? Get World Eater veterans for a bit more with a truly fearsome statline, at the price of not holding objectives.
Specific legions should get style-based perks, yes. Suggestions:
Iron warriors: Extra Heavy slot, maybe the option of carrying more special/heavy weapons in smaller unit sizes. No Daemons.
Emperor's Children: Sonic blasters as default. All models must have mark of slaanesh. Special weapon options for termies and dreadnoughts.
World eaters: Special rule for Khornate chainaxes (best armor save allowable being 4+). Possible need for leadership checks to prevent Rage rule from taking over. Assault version of rhinos. No psykers allowed; possible favored enemy against psykers in general.
Thousand Sons: Arcane wargear options for sorcerers. Maybe something similar to the necron WBB rule for rubric marines. Tzeentch marked psykers being immune to perils of the warp, as suggested.
Death Guard: Options for poisoned firearms and CC weapons. Choice for nurgle zombie troops instead of cultists.
Alpha Legion: Options to give Scout, Infiltrate and Stealth rule to most units. HQs with rules that disrupt enemy reserve rolls (to reflect their taste for sabotage).
Night lords: Raptors as troops. Special wargear for champions to harm enemy leadership. Accurate deepstrike with raptors.
Black Legion: More army-wide rules for their HQs to represnet better organization and tactics. Ability to take on units from other legions as elite, but from a limited list only. Limited use of drop pods.
Some version of the old veteran skills system should also be implemented for added flavor and style.
Renegades: Special rules for chapters that went to chaos, or just broke from the empire, in more recent times. No veteran rule and more expensive marks, but they could retain some modern SM wargear such as storm bolters, thunder hammers and whatnot.