I know the Lintz family, I can personally tell you she did NOT want to leave. She loved being on the show and was heartbroken to learn she would be killed off. They were never told a "reason" - but I think her becoming a zombie really helped her to get noticed as part of the cast!!
I also noticed you did her bio. Her first appearance was NOT "It's Supernatural" it was "The Walking Dead" in Nov. 2010. She didn't do "It's Supernatural" until the following year. You might need to correct that.

And yet Carl is still there, looking just as much older himself.

I actually heard that it was because of her age. If you notice how much older she looks in the second season from the first (which was only a few days on the show but a year in real life) there was only so much longer she could pull off being that age but I do agree, they used this to make Rick cold.

If you haven't read the comics and don't want spoilers, stop reading now.
Sophia is alive and well in the comics, the writers/producers chose to kill off Sophia as a way of turning the show darker, mainly Rick. If you have been watching the show I guess it worked.