Games played is the only good measure. It is a measurable and specific goal. After 100-200 games, a player knows the basics and is prepared for ranked. They can play the game and may succeed or fail of their own accord. Once they've played those matches, and have enough champions for draft pick, then they should be able to play ranked. If they're good, they'll shoot up. If not, they'll join the many other bronzes who still need practice. I would say asking for 75-100 wins is the fairest way to ensure some measure of competence when they join ranked.
Ranked already does a great job of weeding out skilled/unskilled players. No need to add levelling to try and do the same. More people can play ranked if levelling is removed; percentage distributions will remain similar in each tier. I don't think runes are even necessary for ranked; ignoring them puts you at a disadvantage in the first place and causes you to linger lower on the ladder.
Honestly, 100-200 matches and 16 champions is all one actually needs to play ranked competently. The ELO system is absolutely fantastic because you rank up when you play well and down when you play poorly. It doesn't penalize you for poor performance history and doesn't play favourites either. Improvement is rewarded quickly and fairly. Ranking encourages the same things levelling does, but so much more efficiently. Why waste time forcing players to do more than grasp the basics?
If they are playing poorly, their ELO goes down more than it goes up. If they play well, their ELO goes up faster than down.