Alex Karev is one of the only characters to stick it out in Grey's Anatomy as long as he did. He also had one of the biggest character developments out of the entire show.
I think it's pretty clear when Grey's Anatomy first started that Alex was just meant to be an antagonist. He didn't have much purpose or meaning other than getting under the other interns skin.
But Alex grew as a person in so many ways. When he finally let someone in to love him he became a softer person. He was there for everyone even if he was the evil spawn.
Alex became Mers person after Christina left and became one of the fan favorite characters. If he would have left the show before he met Jo, then the ending that they gave him would have been great.
He fought for Jo. In so many ways, he went to war for her. He was her knight in shining armor and while we saw snippets of him doing the same for Izzie, his story with Jo evolved so much more than theirs ever did.
Jo actually loved him back while Izzie would constantly chase after other people or run away. Him and Jo are the dream couple, and he has grown so much that there is no way he would have left her behind with just a letter.
Izzie will always be a part of the original five, but the original five haven't been around in so long that I have to root for the new people and new relationships and thats exactly what I have been doing for the past six seasons.
Karev should have been having children with Jo, they should be living happily ever after especially since she just fought so hard to get back to a good place after meeting her mother.
I will never understand why they chose to end it the way they did, and I will forever be sad that Karev is now gone.