Elixir timers should start when you respawn
When you have a full inventory, any elixirs you purchase immediately exert their effects. You have to wait until you respawn before purchasing the elixir to get the optimal elixir duration (optimal for anyone with six items). This can add up to a couple seconds to the time you're stuck in base, which is detrimental when when everyone needs to rush out immediately to contest an objective. Also, it's just detrimental in general to the game QOL. Yes, I know it's possible to set up the purchase when dead and buy it quickly while walking out of base, but players shouldn't have to consider small gimmicks like this while trying to optimize their in-game mechanics.
Edit: Specifically referring to oracles extract on Howling Abyss. I primarily play ARAM so I didn't realize they'd addressed this issue for all other elixirs.