New to the TES series, but cant really understand. Do armor, Heavy or Light, have inherent (hidden) penalties to the effectiveness of spells or not. Otherwise I cant see the use of pure mages having robes over light and heavy armor since you can enchant the armor with same stuff as robes have.

Any advice? Clarification?

I don't know about a penalty but mages robes that I have found not only often have bonusses to magic but all seem to increase the mana regeneration by 50%.

There's an alteration talent that boosts shield effects by double if you have no armour. This, assuming you get it, makes armour worthless for a mage even excluding the mana regen hit.

Armor does hurt magic in previous Elder Scrolls games. It hurts magicka regeneration and/or magic effectiveness (damage, duration, etc).

Assuming balance purpose, armor should have some negative effect on magic. But I have not tested it as I am playing a stealth character.

Well my beef is that Alteration and the clunky hotkey system makes it quite cumbersome to keep up (especially with the constant need of recasts..) Armor gives same upside and no recast, just wear and forget, or am I missing something.

Armor has weight. The alteration spells don't.
Plus improving your alteration skill will improve all the spells in the school. Whereas armor skill only governs the use of armor.
Though alteration requires magicka and recasts but armor doesn't require casting, as you have mentioned.

Both have their pros and cons.