Random Drakes Should Never Have Happened
The reason why it should not be allowed? Tampering. It opens up the door to tampering. Riot games can tamper with which drake comes up allowing them a method to control the outcomes of games outside of scripting.
Not only did Riot introduce dragons, but they introduced dragons with disparate rewards, and rewards that work best on certain comps. Based on comps, and during the game, RIOT can tamper with games in order to favor a certain team.
It's no wonder they've done this when in modern sports referees play this role, allowing or encouraging certain outcomes to occur. One of the reasons I've loved esports is because outside from throwing games/scripting, the game truly is in the hands of the players and not governed by a supposed "neutral" party called a referee. I'm not suggesting there are instances of this, but the fact that it opens the door should eliminate this factor.