So, just to kinda clear up some stuff regarding medals and the "pay for medal" rumour that's been going around for years.
Anybody that's hosting any kind of tournament in TF2 is able to create a medal for their tournament, so long as that medal is given out only to those that participated in the tournament. Valve does not care whether or not the tournament has some kind of registration fee, which means leagues such as ESEA can easily give out medals if they wanted to do so. However, the main requirement is that the medals have to be earned, not bought.
So basically, a medal is a trophy. You earn it by competing.
As for why ESEA doesn't give out medals? My best guess, is that they simply don't care to do so. Managing medals for each and every season is a mostly manual task. For starters, you gotta actually design the model itself, and then you have to manually notify Valve that you want to ship a new version of it for a new season. Valve will then give you item ids to use, which you need to then enter into the tool they give you to send the medals out to the players that are supposed to get them. Except, the tool they give you is really just a very basic demonstration on how their distribution api works, so you'll need to modify the tool, or create an entirely new one using their api. Then you gotta find a way to easily gather all of the appropriate steam ids for each and every player into a simple list and input that into the tool for distribution. Repeat this every season indefinitely.
So, can ESEA do it? Yes. Will they? Hell no.
edit: for those of you curious, this is the tool they give you - http://sidular.com/promo_grant.html
It's super simple, and really just a basic html file. ESEA would need to basically create their own tool using the api. That's development time, and developers cost money. Money that ESEA would rather not spend.