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Serious question: does it not fit (with the case closed) otherwise?
It's probably for airflow
It is, the main fan for the whole machine is the one on the right and these machines rely on very little clearance for the fan to work. The slot the GPU is using would usually be expected to be used for a network card. The case itself has no holes/etc for airflow by default there for most models. There's a lot of interesting mods for these cases, usually a bit fancier, but this works.
Temps on these change drastically with the case off.
Had it been a smaller GPU, would it be better?
Barely maybe, the fan would still be right up against a solid wall. There are projects out there to add cooling fans to network cards that would fit in that area. It's just rough, airflow wise.