This is my take on it as well. Out of 17 characters, The last 6 (of 8) have not put a single perk in any armor tree. They wear what is fitting for their character. It all comes down to RPing and just what looks good. The best Armor mods all call for a high end and perked Smithing requirement. That alone is good enough for decent protection.

It's not gimping yourself. by doing this. You are choosing to put those perks into something else. It just so happens to keep the character from being OPd. Armor cap?....Why?

Light Armor is for people that want to loot. Most light armors are near 10 weight, heavy armors, even at low levels, are really, really heavy. Want more stuff? Travel lightly.

My first time through as an Orc with heavy armor and two handed weapons. I smithed legendary daedric armor with the enchantment to be able to carry more. With the berserker skill on top of all of that I don't have to sneak around.

Sneaking is not the Orcish way to live

Having used both... I like both. I also don't like wasting perks in anything that isn't keeping me alive longer or dealing more damage. AKA not taking weight related perks, especially the LA 0 weight perk... it already weighs slightly more than cloths, why waste a perk to save 10 pounds in weight?

I actually went heavy on my mage. Its not like he had big heavy weapons or a shield to carry, so the HA by itself wasn't bad and kept him alive a lot longer. Plus always go with a hood for the 'mage' look. Stamina is also useless for a mage in combat, and most spells are going to create enough noise and light to make sneaking pointless so there is no real downside on a mage.

I don't care for warriors.....

My assassins all light armor. Of course my assassins rarely level their light armor skill because they rarely get hit. The light weight, and being able to sprint longer is very nice. I you plan on abandoning fast travel(I recommend it) light armor will save you a LOT of time.

Also looking at the stats the HAs are not that much better than the LAs early in the game. Iron and Leather are basically on par with each other and steel only being a little bit better. Dwarven is a little better than Elven.... you don't start to see BIG differences till you start looking at comparing Dragonplate and Deadric to well... anything else. By that late in the game you either have smithing or enchant pretty high... and either will make up for LA's disadvantage.

The best armor of all..... Sneak. Never getting hit > getting hit... no matter how awesome your armor is.

I sneak just fine in heavy armor. Like others have said, just need the perks/apparel.

As a high level there won't be much of a difference. So..

In my experiences, light armor has better perks, while heavy armor's pro is it's raw AC.

Is RPing enough of a reason for you?

Well, you'll always be a sneak-thief in the eyes of so many town guards, may as well dress like one. To answer the question in the title: because it's light and it's armor.