league-of-legends
While watching the League of Legends tournament teams ban between 3-4 champions, you'll see picks like Eve, Xerath or someone very atypical of tournament play.
Someone will do this while the rest of the team goes serious picks. When they remake the game (which I also don't understand the perpose of) they do joke bans and inevitably the person with the Eve (or whichever) will pick someone else.
Why do they do this?
The setting of League of Legends is on the world of Runeterra, specifically the continent of Valoran. There are two primary city-states, Demacia and Noxus who were constantly at war. The League of Legends was formed in order to control the conflict.
For more detailed information, you can read through the Journal of Justice, which is a sort of ingame newspaper that chronicles goings-on in Runeterra from an in-character perspective, talking about the various Champions, events, etc.
If you'd like a super-quick crash course, you can watch Total Biscuit's LoL Lore-In-A-Minute.
There are a couple of champions who have "latent" trap-like abilities. Testing has indicated that most already placed traps benefit from leveling up, but others (specifically Maokai's saplings) do not benefit from leveling it up.
Original Answer
I coerced my friend FallenAngelEyes into helping me test this out with Maokai and his saplings (alas, I do not own Caitlyn).
This is from the level 1 sapling. Nasus takes 64 damage.
I then threw another sapling, then, after it was thrown, leveled up Throw Sapling to level 2.
This did 63 damage, so leveling up sapling toss after the sapling is already in the world has no effect. Compared to later testing, THIS IS THE EXCEPTION!
(Note:That sneaky Nasus gained a level between tests, and increased his magic resistance enough to mitigate 1 damage! Jerk.)
Finally, I threw a 3rd sapling, from level 2, to establish a baseline at the second rank. As expected, it did more damage.
But one ability on one champion doesn't tell the whole story. I then re-ran the tests with Teemo and his traps, and leveling the ability did update existing traps. Teemo and Maokai got different results!
Shaco, Caitlyn, and Nidalee's traps all scale retroactively as well.
The behavior seems intended that traps scale retroactivley - 'tis only Maokai (who was, unfortunately, the first one we tested) that doesn't adhere to this.
Best Answer
First of all, let's clarify the question. This situation will only happen during online tournaments. During offline LAN events, players have infinite RP and IP as well as every champion purchased. During online tournaments though, players use their standard LOL profiles. As a result, there is a decent chance that some summoners will be missing heroes. When that happens, a placeholder champion that never gets actual play like Eve is chosen instead and replaced with the intended hero later on.
As for why they don't just pick the heroes as soon as they are available? In the current meta, the top and middle lanes are solo lanes. Since solo lanes are 1v1 battles, having to face an enemy who counters you can be too much to overcome. As a result, teams try to pick these two lanes last, in order to avoid getting countered.