As a compeditive sport you can make games random but not easy. However changing the UI Makes different skills useful which shits the balance of power as well as the learning curve. Much like how the ideal GO and Chess players have related but different skills.
The evidence of systems like Relic RTSes (Company of Heroes, Dawn of War, etc) indicates that even when you make the system easier to use, micro skills just shift to something else. In DoW2, for example, the skills that in SC2 make controlling a bunch of marines and macroing even possible make for sophisticated flanks and clever lures that are IMHO far more interesting to watch. Very sophisticated grenade play, specialized suppression mechanics, and doing five different things at the same time with your units is actually expected at high levels of play, whereas I can count the number of times I've seen a major flanking maneuver in SC2 on the fingers of both hands.
Introducing randomness is honestly a poor choice in competitive games. Warcraft 3 random item drop, Starcraft: Broodwar Scarab glitching & high ground random miss percentage, etc all made the competition somewhat less compelling.
Poker at the very least is played for EV and moves are made with the expectation of the randomness converging over many samples. This is partly why tournaments are considered luckfests by most money game players since you need to win so many coinflips to win.
Well nothing prevents the game designer from implementing similar mechanics (lots of smallish randomized events in each game which will lead to variance reduction)
There is probably an interesting distinction to be made between the type of randomness that comes from a deck draw versus the type that comes from a loot table... but I don't know it. It feels different, but I can't quite put my finger on what it is.
I'm not convinced of that. In either case, the random element just makes the game tree larger.
What I like about randomness, is that adding it makes each of the individual games a unique story, which can have a great appeal (just look at the success of MtG,or Binding of Isaac for example). Obviously, designing such games (so that they're balanced) can be an order of magnitude harder than designing a game without randomness.
