Very bad SDL2 performance on Hyperpixel Square

I have a hyperpixel square, and want to create an application using SDL2. But the performance is very slow. Even if I don’t draw anything (just a loop that does nothing but clear and present an empty renderer) I can’t even reach the minimum of 20FPS for my program, it’s stuck somewhere around 10-11FPS at best.

Is this a known limitation of this screen? Or am I doing something wrong? I’ve read somewhere that if you use GPIO instead of HDMI you cannot use the hardware acceleration of the GPU. Is this true? Even so: With CPU rendering I still would expect more than 11 FPS.

Can anyone give me some pointers in the right direction?