I was confused with a different concept, disregard that part. FFT is by definition reversible for a discrete signal like a quantized image so each pixel must be

I was confused with a different concept, disregard that part. FFT is by definition reversible for a discrete signal like a quantized image so each pixel must be reversible, so it has to be 4x total space used with no further operation, correct. Quantization and filtering are the more important parts of the encoder than the FFT / DCTs since the transform is 1:1 reversible. Compression isn't just the mathematical accuracy of a signal when it comes to lossy algorithms as you know. A 720p video upscaled to 1440p should theoretically be exactly the same size for the sake of effective quality but encoders don't care about just the math and apply perceptual filters because simply doubling pixels looks really bad perceptually it turns out.