Everything is relative, right?

Instead of thinking about a tilted lens, think of it in terms of a tilted film plane.
And take it to extremes: tilt the film plane 90 degrees.
Then you'll notice that the side it presents to the cone of light coming from the lens is as small as the film plane is thick.
So the image circle doesn't grow when you tilt a lens, but the film format, as seen from the lens, actually shrinks.

So no coverage problems with tilts.
Tilts do not require a larger image circle (which is why, for instance, the regular Zeiss/Hasselblad lenses work perfectly well on the FlexBody - if only people wouldn't think it is a shift camera, which it is not). On the contrary: coverage could be less, the image circle smaler, and still cover the full format.

When you tilt the lens, the image circle shifts. Shift is then needed to put the film plane back inside the image circle.
But the image circle does not need to be bigger.