I am not an expert on this, trained in physics not electronics. When you look at a low rep rate signal at 500ps/div the beam is on a very small fraction of the time, about 5ns every msec so one part in 200000. The readout is being triggered automatically and runs around 1kHz or so, I don't remember the actual clock speeds. So for the same brightness the signal trace has to carry maybe 1000 times the current compared with the readout, this means a higher density of electrons and the space charge can affect the beam focussing compared with a low current beam.
I tried putting a fast rise square wave into my 7904 at 1kHz and qualitatively I see what you see. I have to turn up the brightness a lot to see the trace at 1ns/div and it does defocus compared with the readout. I can improve the focus slightly and that worsens the focus of the readout significantly.
Maybe if we get some more comments we can decide who is unrealistic and who is easily satisfied. I have no idea what the factory specifications were.