What is better? All carry beeing viable or only ranged one?

Not sure what you're talking about. Some of the biggest carries in the game are melee carries... Nasus is about as strong as it gets late game (build full tank and solo the two nexus turrets while 5 people are trying to kill you).

If you're referring to the ADC role... it's better to have only Ranged ADCs be viable.

I mean, think about it. You're creating a champion who's meant to deal high sustained damage to both champions and structures. A ranged ADC does this by ignoring defensive stats and relying on their ability to position, re-position, and kite their enemies in fights. They take down structures by attacking from range while the front line stands between them and the defending enemies to deter them being dove.

Now take a 'melee ADC'. He needs to get in to the middle of the fight to deal his melee range damage. So you have 1 of 2 options:

1. He retains the classic "adcs are squishy glass cannons" concept, and is easily targeted and quickly destroyed as soon as he gets in position to do his own damage.
2. He gets some way of having survivability when within melee range (he can tank some damage), in which case why would you ever choose a Fighter who does the same but only puts out a fraction of the damage?

There are a couple exceptions to these rules. Take Tryndamere, Fiora, Master Yi, and Talon as examples. Tryndamere gets those few seconds of surviving from his ultimate. He's as close to a melee ADC as it gets and he relies on cheese. Fiora gets untargetability during her ultimate for a few seconds. She can dish out great damage in fights but won't be much help trying to siege a structure. Master Yi gets short but frequent untargetability from Alpha Strike as well as a huge MS boost from his ultimate. Similar to Fiora once he's reached late game he'll do well in fights but again he can't do much sieging a turret. Talon has stealth and a dash which are great for fights and even backing out from a turret. It's why he's the only melee ADC you see ever go bot lane in lieu of a regular adc. It's still a horrible decision because of the last problem: Ranged champions are stronger in lane than melee champions are because of their ranged harass. You think Caitlyn can harass Graves or Vayne to no end in lane? Try playing Talon against her. When you're in a 2v2 lane that heavily relies on building CS throughout the early game to reach your late game power, playing with a ranged disadvantage is just ridiculous.

Just all-in-all, ADCs are right for the game. They provide a core function to the team that cannot be provided by any other type of champion without making said champion grotesquely overpowered. By definition, making a melee ADC viable would make them invalidate every fighter in the game. At a time where Fighters are among the strongest class of champions, even implying that it should be considered is laughable.

Riot doesn't like Melee carries that can just get up to you and right click you to death. They like melee assassins instead.

EDIT: The other thing is, Melee Carries are generally too squishy and end up getting killed before they can get in range. Which is why many are assassins.

Dota 2 pulls off Melee carries because of how stats work. Carries build a stat that will give them damage as well as some form of defense. This allows them to have some survivability in the form of innate tankiness. and how Magic Resistance is not a common stat (and thus is how to deal with even the most fed carries in Dota). This means that no matter how "Tanky" the enemy carry gets in Dota, until he buys a BKB, he's vulnerable.

I think he's tryng to communicate