If you smith, you can improve either up to 80% physical protection. So, the difference in protection is only at the beginning. The weight/speed penalties go away with the Steed Stone, or perks like Conditioned/Unhindered late in the game, but Light gets them at a lower level, and cost less perk points over all. Heavy Armor can also be perked to reduce Stagger, and Falling Damage, while light fortifies Stamina recovery, in addition to any Enchantments.
Muffle eliminates the penalties for sneaking in Light Armor, but once you get Silent Movement (Sneak) they're moot. As far as playstyles go, you can't "Never get hit," even with Stealth, though you can come pretty close with Illusion. I guess you can technically savescum by returning to your last save every time you get 1 shotted, but it's not even remotely an all, or nothing thing. If you're evasive, then Light Armor basically makes up for you not having a lot of Health early on, then eventually protects as well as Heavy.
If all you care about is damage reduction, get a Breton, go Heavy, and never look back. There are other Stats, and they're in the game for a reason, though. If you Sprint, you can go Longer/Farther in lighter gear. Regardless of whether it's classed as Light, or Heavy, the more weight you have equipped (Including Weapons, and/or a Shield) the more Stamina it takes to Sprint. Also, certain types of weapons/armor slow you down when equipped, Heavy Armor, and 2 Handed weapons the most. While you may believe something like "I don't have to evade, because I'm a Tank!" not all of the game is in combat. Quite a bit of it is running cross country, or riding a horse to get to the next Quest/Location/Fight. I find it kind of sucks only being able to Sprint a second, or two, then waiting several minutes to recover, so for me Light is the weight to go. (Or the lightest Heavy, Wolf Armor.)