The main reason is design, not simply the mirrorless mount distance.

The EF 70-200mm f/2.8 is an internal-zoom lens: its physical length stays the same as you zoom. The RF 70-200mm f/2.8 uses an extending zoom design, so it is much shorter when stored or at the short end, but lengthens as you zoom toward 200mm. That’s why it looks dramatically smaller in comparisons.

So your intuition is basically right: the short flange distance of mirrorless bodies is not the key advantage for a telephoto zoom like this in the way it often is for wide-angle lenses. The compactness mostly comes from Canon choosing a different optical/mechanical layout.

The trade-off is straightforward: you gain a shorter collapsed lens, but you lose the constant physical length of an internal-zoom design. In practice, the RF lens extends while zooming, and at 200mm it can be about as long as, or slightly longer than, the EF version.

So Canon didn’t necessarily “give up” image quality or speed here; the obvious compromise is the extending barrel design rather than internal zoom.