The first perks of..
one handed
two handed
sneak
archery
Enchanting
Pickpocket
Heavy armour
light armour
Alchemy
block
Why? Well firstly these perks increase the skills effectiveness by 20% (out of 5, so to a hundred percent) However the skills for most of these do very little to change how effective the act is! So in a way these perks actually replace the skills!! The skill number is used only to tell you which perks you can pick up.. Is that even Elder scrolls? Half of the skills do this! Wouldn't it be better for the player to Not have these perks and instead improve the skill with the actual skill level? Some of these perks downright take all of the skill whilst one or two arent so bad (i am thinking sneak and speech, but they increase by a value less than 20)
Secondly the chain perks for
Destruction
illusion
conjuration
Lockpicking
alteration
Restoration
Arguably smithing
(by this i mean that there is separate novice/apprentice/journeyman/adept/master perks)
The magic skills for instance only loose 33% of their cost at level 100 and the perks half that. But that's just.. stupid! Firstly you NEED perks if you are going to use high level spells! (in destruction you actualy Need enchantments too due to the expert spells costing about 100 magicka and need to be used in quantity.. you are going to need a [censored]load of magicka to take down something your level in one go and chances are you're going to have about 300-400 at that kind of level if a pure magic user) But wouldnt it be easier if you didnt have to waste perks on these because magic Actually became a lot less costly and Lockpicks actualy became easier to pick with leveling?
What if i had 100 skill and no perks?
What if i had 50 skill but the first 3 perks, making me a better user of that skill than the hundred guy?
Will this novice lockpick perk help me at all in journeyman locks?
What if i had 100 illusion, no perks and wanted the perk that makes all my spells in other schools stealthy from the illusion perk tree?
What about when i get 60 one handed and 60 light armour in the same level- i will need to pick only one of these to actually improve! The other can wait for the next level up so long as i dont get my Enchanting to 60 then!
I like these posts..

I agree. I had expected perks to act as with Fallout 3, where they provided substantial and different mechanics that complemented skills - not substituted the role of skills themselves by taking away their incremental increasing of the effectiveness of the relevant mechanics and adding them in as perks (which makes skills pointless, since as you noted their only role now acts as milestones to unlock certain perks, which is quite silly).Yeah, I really dislike the new levelling system. Oblivion's was better.
The fact that most of these bland +X % perks are needed to make the skill worthwhile actually shows quite well where the problem lies that the OP mentioned, just that in this case it's not the perk which is redundant, but the skill itself, as it's basically no longer needed except to unlock the perk.