I'm not an astronomer but I think we only get the cool corona effect because the whole disc is blacked out. But maybe.

When the Moon was closer there would have been a distinctly Cthulhu moment where the corona appeared on one side of the sun as it blacked out. Tentacles!
1
0
1
The moon has been blocking the whole disc since it formed, but earlier it would have been blocking out more of the corona at the same time. Eventually it will move far enough away that full solar eclipses are no longer possible.

But yes, maybe tentacles on the one edge, then on the other.
1
0
1
The question was about what happens when the Moon covers less of the disc. Would we get better views of the corona? And I don't really know. Would we get a corona at all if total eclipse isn't possible?
1
0
0