I like to muck around with a program called Sketchup - basically it's doodling in 3D, I like doodling stadiums and stuff because I'm a frightful bore.
Just for thought experiment purposes, I went and found a quite neat looking model of Bluetongue Stadium, because I wanted to doodle what a new roof *might* look like if someone were so inspired and well funded as to want to build one.
The existing stadium looks roughly like this - this model isn't exact, it's just "close enough" to give you an idea of what things look like:
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and with a new roof (basically a big arch roof that wraps around the stadium in a big circle that's cut out for the field and the road):
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This isn't engineered or anything, I ain't an architect or an engineer, I'm just doodling. But a new roof could be designed to basically sit on top of the existing stadium and cover all seats as they are. It need not be massively tall or ornate, it just ought to cover the stadium against rain etc.
Presumably you'd go and send a bit on other infrastructure while you're at it, but f the place were covered and sheltered, people wouldn't look out the window and go "bugger that, not going, I'll get wet".
It'd also keep atmosphere in far better.