By that logic the burden of proof is on you, the one suggesting Bethesda change their system, rather then on me, who is advocating it stays the same. But I will play your game regardless.
As mentioned before, the difference between having all the +20% perks, and missing one, on the best sword in the game, is 3 damage. There are a number of ways to make up for that,
-First off is enchants
--Absorb health enchants do anywhere from 5-25 points of HP damage. Meaning even the worst ones utterly negate at least one +20% perk, while the best negate the need for 8 +20% perks, which is more then there are in the game.
http://www.uesp.net/wiki/Skyrim:Generic_Magic_Weapons#Absorb_Health
--Fire, Frost, and Shock enchants deal anywhere from 5 to 30 points of damage. Meaning they can negate the need for anywhere from 1 to 10 of the +20% damage perks, again, more then there are in the game.
http://www.uesp.net/wiki/Skyrim:Generic_Magic_Weapons#Fire_Damage
http://www.uesp.net/wiki/Skyrim:Generic_Magic_Weapons#Frost_Damage
http://www.uesp.net/wiki/Skyrim:Generic_Magic_Weapons#Shock_Damage
--Fortify One-Handed enchants, which do anywhere from +15%, to +40% skill effectiveness. Meaning one can negate needing to take up to 2 of those perks from just one item, not to mention you can have several of these items at once, a necklace, ring, and gauntlets, allowing the player to negate the need to take up to 6 of the +20% perks if they have all three items.
http://www.uesp.net/wiki/Skyrim:Generic_Magic_Apparel#Fortify_One-Handed
-Second is smithing, which can improve a weapons damage by up to 10 points, assuming you have zero of the +20% weapon damage perks, as the damage increases get weird if you have one or more of them, as it all stacks.
http://www.uesp.net/wiki/Skyrim:Smithing#Item_Quality
-Third is potions and poisons, which can do everything from boosting one handed damage by 50%, to dealing up to 65 points of HP damage on a target when hit.
http://www.uesp.net/wiki/Skyrim:Potions#Potions
http://www.uesp.net/wiki/Skyrim:Potions#Poisons
And this isn't even getting into this like unique weapons, artifacts, leveled items, and other magic items like scrolls, all of which offer their own unique bonuses, many of them damage related, that can make up for not having some or all of those +20% damage perks
http://www.uesp.net/wiki/Skyrim:Unique_Weapons
http://www.uesp.net/wiki/Skyrim:Artifacts
http://www.uesp.net/wiki/Skyrim:Leveled_Items
http://www.uesp.net/wiki/Skyrim:Scrolls
In short, you basically have to avoid 90% of the game to actually have not having one or several of those +20% damage perks actually make the game noticeably harder, as the game gives you SO MANY things that deal damage that not having all of those perks basically becomes a non issue beyond a trivial few more seconds of hitting M1 at the enemy.
And again, this is all with the best one handed sword in the game. With lesser weapons, the +20% perks offer even less damage increases, meaning these values only negate the need for those perks to get equal damage with said weapon if you did have them all, even more.