The power of the class is important.
Since Klinda was a focus of the OP, I'll stick with that. Season 11 warriors were very weak. Colossus smash was nerfed for pvp (was a full 100% in s9) among other things and frankly other melee classes just outshined warriors (rogues were ridiculous, paladins had tons of utility and off heals, necrotic strike stacks were super deadly against healers, feral druid survivability was off the charts).
I think the most important thing in arenas is comp. Playing with the right amount of CC that doesn't DR together, the right amount of healing and damage, etc just makes things so much easier.
I want to say that in 85 arenas gear isn't much of an issue. After a few months, just about everyone at the high ratings has full conquest pvp gear. However, season 11 left me feeling a bit sour. The pve trinkets from Dragon Soul and various weapons (heroic gurth / legendary daggers and staff) were ridiculously OP. A heroic cunning of the cruel was brutal in 3s, but it scaled with the amount of players you were facing, so it was much, much worse in rbgs. Get 2 locks, 2 spriests, 2 boomkins all with heroic cunning of cruels with 3 healers and a tank into 10v10 rbgs and you could probably coast to 2.2k+ with ease.
Skill is still important though. Even with the best comp and the bis geared characters all around, if the you and your teammates are trash, you're going to get stomped before you get too high. You still might make it higher in rating than some people believe you should, but I doubt you'd make it to gladiator or even duelist.
In twinking and especially f2p, I feel like less skill is involved. Classes have fewer abilities and cooldowns to manage and thus fewer ways to counter other classes' abilities. Certain classes can practically one shot others (hunters before, hpals briefly, etc). There is so few stats that maxing out those stats with the very best gear is very important.