I'm going to take a different tack on this question.
At sufficiently high levels, (vanilla) Skyrim is poorly balanced. Although anyone can play at Master or Legendary before then, that's not really what those difficulty levels are for. They are band-aids for an unbalanced post-endgame.
I realize this is a potentially controversial assertion, so let's walk through some of the more blatant and serious imbalances in the game:
- With very high smithing and/or armor skills, you can get to the armor cap, at which point all damage is reduced by 80%.
- Any enchantment can be placed on any unenchanted armor, with no change in effectiveness, so hitting the armor cap need not interfere with any of the following strategies. In particular, mage robes carry no advantage whatsoever over custom-enchanted armor.
- The Lord Stone provides an extra 50 points of armor towards this goal.
- Blocking caps at 85% (physical) damage reduction and stacks (multiplicatively) with armor, meaning a successful block, with a character at both caps, will only take 3% of base damage.
- You can get to 85% magic resistance, which stacks with armor (but only works on magical attacks).
- There are several slotless sources of magic resistance, particularly an Alteration tree perk, The Lord Stone, and a sidequest.
- You can get to 85% elemental resistance in each element, which stacks with both armor and magic resistance (but only works on attacks of the appropriate element).
- Dunmer and Nords get 50% slotless fire and frost resistance (respectively) for free.
- Vampires get some frost resistance and some fire weakness depending on their satiation levels. The buff and debuff effectively cancel in the enchantment slot calculus (i.e. you need one more slot for resist fire and one less for resist frost).
- As any race, you can get to 80% spell absorption by combining The Atronach Stone with the Atronach perk (in the Alteration tree). Bretons can temporarily hit 100%, although this is more of a parlor trick than a serious piece of any build. Spell absorption works differently from all of the above effects (it's all-or-nothing and probabilistic), so it stacks with them.
- The Lord Stone may be combined with The Atronach Stone using the Aetherial Crown. With high enough smithing, a "proper" headpiece is not required to hit the armor cap (nor indeed is The Lord Stone, of course, but the slotless magic resistance is another matter).
- When all of the above buffs are combined, the vast majority of "reasonable" magical attacks are harmless, or nearly so. Karstaag in particular goes from a super-powered bonus boss to a total pushover with a mildly dangerous melee attack.
- With sufficient enchanting skill, you can get to -100% magicka cost for any spell school of your choice. With Extra Effect, you can do this in two spell schools. Since this takes up a lot of valuable enchanting slots, it may interfere with the previous bullets. But, it gives you the unlimited ability to spam some very powerful spells, and completely eliminates the need to have a big magicka pool.
- Both magic resistance and elemental resistance can also be done with alchemy, which does not consume enchantment slots but is a bit more annoying to work with. Alchemy can also make spell schools more powerful, which synergizes with the previous bullet, and it can provide a wide variety of miscellaneous buffs and debuffs.
- Over time, the average player will build up a large set of permanent buffs, which tend to be less game-breaking individually, but collectively do have an effect on the game's balance.
- Argonians get Histskin from the beginning, which provides 10x healing rate for 60 seconds, once per day. At lower levels, this can substitute for a large chunk of the above defensive strategies and basically makes you immune to death by any means other than a single massive attack.
- Vampirism carries both strengths and weaknesses. However, the Vampire Lord form is so ridiculously powerful that it arguably negates most of those concerns outright. From level 41, its Drain Life spell does a base damage of 150, plus draining 25 health per second plus also draining equal amounts of magicka and stamina with Blood of the Ancients. For this, it costs a paltry amount of magicka relative to every spell in the Destruction school, and it is clearly intended to be spammed, as it is permanently equipped to your right hand.
- You can use enchanting to buff alchemy and vice-versa, and neither of those effects are capped. Alchemy and enchanting can then be used to create arbitrarily strong buffs of many different kinds, as Skyrim leaves a lot of other stats uncapped. Some people would consider this cheating, but Bethesda had a lot of time and opportunity to patch this out, and never did.
- Mods tend to exacerbate rather than improve these issues, unless they are specifically focused on balance.
Most of these strategies don't really top out until your character level is in the forties or fifties, at the earliest. However, you can start working toward them a lot earlier, and if you are doing enough of these things simultaneously, your character may still end up "too" powerful relative to the leveled enemies.
So, yes, you can play through the game on Master or Legendary, but that may not be as much fun as playing through the game on Adept until you get bored, and then cranking the difficulty up as needed, when needed.