A bearing in a yoyo is easily compared to a belt and pulley system, where the size of the bearing (pulley) allows a mechanical disadvantage to be realized. Since the D bearing has a smaller diameter than C, it has more mechanical disadvantage.
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But it’s not just the bearing that’s spinning, as it’s mechanically connected at the inner race to the yoyo. It would spin a bit faster as the radius that the string comes off is slightly smaller. The rotational inertia would be everything that’s spinning, not just the bearing.
PS
Look at a flywheel, the large moment of inertia comes from the weight of the flywheel, not the bearing that it rotates on.
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The mechanical (dis)advantage happens when throwing the yoyo, similar to starting a flywheel. The larger the diameter of the bearing the easier it is to pull, the smaller, the greater the speed you can get out of it (provided the mass of the flywheel isn’t too great).
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The bearing will have something to do with inertia because its smaller diameter will increase angular velocity.
I fail to see what you are confused about then. A lighter throw on a D-bearing yoyo will spin the yoyo at a higher RPM as compared with a C. I think C-bearings have been the objective choice in a yoyo because of the RPMs. It spins slower, so is less effected by movements to slow it down (as in it doesn’t matter as much). Do one of your average casual tricks smoothly, and you won’t lose spin. D-bearings are fun because if you can maintain the RPMs, the binds are tight and satisfying, and if you did everything well your yoyo is still spinning faster. Id personally choose a C-bearing in a more competition oriented yoyo, but as it turns out D-bearings seem to perform pretty well in comparison to a C, and just have a different feel.
Id argue that you CAN make a D-bearing performance yoyo that is up to today’s standards of C-bearing throws, but misses and sloppy play will hurt you more, which is less than ideal. In the end, inertia killing moves are more devastating on a D-bearing, and anything larger diameter than a C would add centerweight and probably spin too slowly to get a tight bind out of. It is almost like yoyo designers have thought about this 
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This explains why I am so not an ideal D-bearing thrower.
I don’t have any D bearing yo-yo’s, and I swear looking at the Don in Expert’s store I would swear it’s large.
Can some throw a picture up an A , C and D next to each other?
I’m sure I’m not the only who can’t visualize them.
Thanks
From a conversation about bearing blanks.
Width can be a little more complicated.
A bearing is MR105: 5 x 10 x 4mm
C bearing is R188: .250 x .500 x .187 inches or 6.35 x 12.7 x 4.7498mm
D bearing is 658: 5mm x 11mm x 5mm
but…
A bearings have a 3mm wide version.
C bearings have a half-spec version (that is wider than half), 0.125 in wide or 3.175mm.
D has a 4mm wide variant, MR115, and a 3mm wide variant, 685.
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Thank you