A little bit of "all of the above" honestly. As a general rule, most of the three-word damage shouts in Vanilla Skyrim are balanced around being level 20-ish on adept. Using the Blood Dragon as an example enemy, it's a level 20 to 29 dragon with 1400 HP. If it's not a fire dragon (as dragons resist their own element) and you have Augmented Flames and The Fire Within, a three word fire breath shout (assuming that you beelined to get all three words rather than meandering through the game) takes off about 13% of its health at 100*1.5*1.25 = 188. With about 50 weapon skill, 40 smithing skill, Savage Strike, and the armsman perks, your Elven Sword is dealing (1.25*(10+5)*1.4*2*1.25) ~66 damage as a sword and board character. So one fire breath = three swings, assuming no enchantment. It gets a benefit in that it is unblockable and has range, but it can only be used on a very long timer.
Now look at how much damage that is against a level 50 dragon. Those dragons have three times the HP; they also are more likely to kill off any NPC support, as their breaths deal 5 times as much damage. Your full fire breath is now only doing about 4% of their HP in damage, but your sword - and bear in mind, we haven't considered enchantments or poisons at any point - is doing... 100 weapon skill, full smithing, full armsman, daedric... (26*1.5*2*2*1.25) 200 damage a swing. Your fire breath is now strictly inferior to a weapon swing.
This only gets worst past 50. Past 50, a character who was focused on one skillset will have to start seriously exploring new skillsets to level, and two more crafting trees are tempting targets since they don't require starting over with a new primary combat skill.
Why do I use weapons as the basis for comparison? Because breath shouts clearly have melee characters principally in mind; they interfere with the flow of combat less for melee than ranged, and zero shouts in the default game offer any specific synergy to magic characters.
Why do I use Blood Dragons as a balance point? Because most people who finished the main quest were in the neighborhood of 50, so 20s would put you right in the middle of the game, the part where game designers are traditionally most concerned about keeping someone's attention as far as balance goes, Dawnguard and Dragonborn content assume a start of level 10 to 20, and Blood is the first tier of dragons that you'll encounter that can assume you've got more than rudimentary skills.
Now, let's assume you get the Soul Cairn shout... ever. I mean, ever. It does 300 damage, and isn't subject to elemental resistance. So it's relevant long after Fire Breath stops being relevant, and it's flatout one-shotting your average bandit for quite a while before it can't anymore. And it does more than just damage. Its cooldown is shorter than Fire Breath. So if you get a hold of it anytime before your 40s or 50s, you have to actively choose not to use it, or you're just going to steamroll things.
That's why the breaths aren't balanced with respect to level. That's why I make Fire Breath level up with you, and that's why other shouts which are already strong are leveled *down* with you, too. When most everything else in Skyrim levels up with the player to some extent - damage, efficiency, enemy health, loot - it seems like a tragic oversight that shouts don't, and they cease to offer the legendary power that the dragonborn is supposed to have. Increasing power rather than constantly decreasing cooldowns feels more true to the designers' intent; there are only three readily accessible shout reduction items in the game, and they ask you to give up a lot for them.
With respect to difficulty - frankly, it is difficult to balance ANYTHING with regards to this many difficulty levels when your only change is a damage multiplier in/out. Nothing is balanced with even the slightest hint of optimization at the lower skill levels, since the same character on novice is doing eight times the relative damage as he would on legendary. I figure that a lot of people are like me, and I want challenging fights, but I don't want every encounter to take forever. High difficulty rating (meaning I can die easily) keeps me on my toes as armor caps out relatively early, and powerful abilities on longer cooldowns allows me to make quick work of weak encounters, as well as providing moments where I can turn the tide of a difficult battle - or mess up and fail to do so. Still, it actually should be fine on the lower difficulty levels until 50+. That's about the point where I think scaling on weapons becomes a quadratic mess for most people and many spells cease to be effective.
There is no way to simply provide powerful abilities on long cooldowns that are relevant to master and legendary (expert is more of a convenient byproduct) and won't break the game from novice to adept. Playing at those difficulty levels, to me, implies that you're actively going to curb how you fight and prepare for fights - e.g. "My character's not a smith, thinks enchanting in Tamriel is abhorrent, and can't use alchemy." That said, talking about all this gave me an idea on how I can make this module easily scale down for those who play on lower difficulties.