I'm ignorant to the subject, but is it too difficult to grow real turf inside a stadium?
It's not really "difficult" per se; we've come a long way in simplifying the process. Having an indoor ecosystem the size of a football field definitely has plenty of challenges beyond run-of-the-mill landscaping though. It also requires a very expensive infrastructure to set the stage for what turns into a huge horticulture project.
Beyond the football, you'll need an elaborate plan to protect the grass when hosting other events... which was one of the big selling points of building a dome in the first place.