Everyone seems to be complaining about the death of melee carries, and I personally think the answer is in items, not kits.

The problem is that melee carries need high movement speed and are completely shut down by cc and burst damage.

To bring back melee carries we therefor need items that give movement speed, stacking tenacity, and possibly better effects on melee hit or mini poppy passives (resistance to burst damage). I personally think maw was a step in the right direction (helping to prevent burst damage kills from mages), but that we need some type of tenacity item geared towards melee carries.

Cloak and Dagger...
It has Tenacity...
It has Crit/AS...

PD or Tri-Force have MS, Cloak and Dagger or Merc Threads have Tenacity...

The items are there already, you're just not buying them for some reason?

People could play Malphite as an AD Carry.

He has the potential to pentakill a team before they can get a chance to react.

Melee carries are bad in LoL because they have no advantage over ranged carries aside from having more damage. They do most of the work of killing themselves for you because they have zero positioning.

By comparison, melee carries in DoTA2 are perfectly viable because most items have increased stats or unique passives for melee heroes. That, and Black King Bar which gives temporary near-immunity to crowd control and magic and pure (true) damage.

Melees in League have a noticeable disadvantage to Ranged. While they have (slightly) stronger steroids and (slightly) better defensive stats, they have to get into range to start dealing damage, and that unfortunately puts a squishy target into the fray of combat. So, unless your team has a mass disabler like Galio or Amumu, melee carries can NOT function in a team fight because the moment they're in range to attack, they're in range to BE attacked.

And who's NOT going to attack the glass cannon instead of the cement wall?

As he said, if you really are worried about constant death get maw and cloak and dagger. if you need armor, depending on champ, randuins omen is amazing for when you do close in, that slow that it does can surely change the battle.

lastly take advantage of frozen mallet, if you are seriously worried about death and you team has no formal tank, try this:

Frozen mallet, Atmas impaler, Maw of Mal, Cloak and dagger, Infinity edge, and berserker greaves.

Thats 20% attk speed from Cloak and 25% attk speed from berserker greaves so your attk speed is fine.

20% crit from cloak and dagger and another 18% from atmas and another 25% from infinity brings you past the 50% mark so you WILL crit.

and about all except for boots and Cloak do meele damage so your damage output wont be down.

you can consider this a BASELINE build for any meele champ whom does not desire death.

The problem is that melee carry doesn't even exist. You have to play bruiser which means, you need good spells like riven, renekton, yorick.

A champion like master yi or tryndamere doesnt have the team utility to be bruiser, but melee carry doesnt exist in the meta, so they are just, useless. There is no room for them in LoL.

EDIT: Also, it is hard to buff melee items or melee in general because top lane bruisers are strong enough as it is (they have good sustain spells, gap closing abilities, burst abilities, stuns, dashes, etc.)

So in order to buff the average "melee carry" of the old days, you would need to change the meta.

And what kind of ADC has no armor pen items ^ ^

I think kits is where melee carry fall short tbh.

Take a look at Fiora.

Her passive is a joke.
Her lunge needs a target so she can't escape with it.
Her riposte active only reflects a single auto attack (pathetic!) and the AD it gives is meh.
Her burst of speed only lasts 3 seconds and doesn't give mobility unless she hits someone.
Her blade walts is amazing, but she can't control who it hits or where she will be when she exits it.

A melee carry needs the ability to avoid a burst or cc. If Fiora's riposte blocked the next spell, then she might be a viable carry...

I realize that cloak and dagger is a good tenacity item, but 35 tenacity isn't enough for a melee carry because they have to be in the middle of the fight. Most/all of a melee carry's survivability is lifesteal, which is 0 when they are stunned. Making a stacking tenacity item geared towards melee carries would give them a way to get around this issue and wouldn't necessarily be broken for ranged ad carries (as they don't need as much cc reduction because of their range).