I'm going to copy & paste comments I made to the sovreign in another post.....generates more conversation.
I agree that the Sovereigns need to be better indicated as "more" than their champion counterparts. Otherwise, why don't we have 35 factions? These sovereigns are world-benders for a reason.
I agree that a large portion of the solution lies in how they handle magic, but would be very against the "all sovereigns have all schools" method of doing so. First and foremost because of how it would dilute both the ability to gain higher level in magic without focusing on it to the exclusion of other things (5 schools filling up your trait pool at random instead of 2-3).
I feel that the solution lies in two things in terms of the magic aspect, and then others as indicated above.
First, sovereigns should be the only units casting global, city enchant, or strategic general spells. Those guys are badass spellcasters and the BREADTH of power that suggests helps support this. In addition, it helps limit what sort of access a given sovereign will have to spells in a given game (can;t rely on finding a Fire Champion to give you Curgen's Volcano). Champions, conversely, should be strictly limited to tactical spells, strategic summons, and unit enchants. They are casters, but not really super powerful ones.
Second. Champions should largely have access to one school of magic, with champions with a second school very rare. I think this is pretty much the case now, but have admittedly neither taken strict notes, nor seen every champion in the game (a testament to the number of champions there are)
Non-Magic Related. I would LOVE, as the OP suggested, to see the number of points we have at sovereign creation to increase, the actual costs of things to diversify, and additional legitimate equipment choices to appear. We do already have some pretty awesome magical choices to start with, but what if we want some standard, sturdy, simple armor?
Totally going to expand on this again, as I've been thinking about FE champions alot lately and have decided to comment.
Love Mal's comments and they all hit spot on.
Your leader should be a 'super mage', the only one eventually able to access all areas of magic (with perhaps the ligh/dark limitations) and be the only one to cast city, global, and epic spells.
Your champions on the other hand, are hired hands, and should be treated as such. War mages should be as high as they get with specialization limited to tatical spells of a single magic type. Keep in mind that champions also have the wide variety of being assassins, warriors, administrators, etc....something that should be limited, but not completely unobtainable from your leader. This setup would require other champions to have a successul empire, but would still give your leader the option of specializing if, for some odd reason, he/she doesn't want to be the ALL POWERFUL mage. 
Leaders should, imo, have way more detail into their design. It is an RPG afterall. The leveling is awesome, but he should also sometimes reach new plateaus of power....apprentice, mage, grand mage, etc; with each tier granting a special global bonus (or perhaps a choice of bonus). An example could be: Choose either access to a new element source type OR +1 combat to all your troop (paltipine style). Once the choice is made, it's possible you never get that choice again so it would mean each game is globally unique.
Additionally, the storyarch (if there is indeed one with this 'fallen enchantress' could/should progress according to your Leader's lvl (plateau power). Cutscenes could be done upon each new level as the story progresses. You as the player then KNOW something is coming...something big. You'd drive yourself to make the leader better in order to fight this entantress....which in turn would press the story on. Just thinking of this now.....maybe the power plateaus should be time based......say like in civ the time duration changes at different ages, in FE the powers you get change at different ages. Just throwing it out there...
Would also LOVE to see some quests that only your leader can do...especially in the mid to late game. That way, you can choose to do your own thing with your leader OR go on this quest. It's a choice. Empire vs Quest. Yet more decisions that you'd have to make.
Anyways, those are my thoughts on the matter.
Hope you can use it.