It doesn't appear to me, watching the many Shioda demos on YouTube, that Shioda sacrifices his ground connection when he is making serious contact with his uke. If you watch the clips, I think you will find that when he's doing his "Shioda Bounce"(TM) and is off the ground while his uke is also not grounded, he is just "helping" uke to complete an arc uke is already circumscribing in the air -- having already been off-balanced. Also, do not discount the very strong possibility that, besides the generous serving of "ham" Shioda often dished out in his public demos, his demonstration ukes did not always wait for Shioda to touch them before taking ukemi for that kind of schtick.
Whenever Shioda is actually applying aiki, he is in contact with the ground with at least one foot or his uke is in contact with the ground and Shioda is connecting to the ground through uke. As far as I can see, when Shioda is bouncing uke off his shoulder or hip -- doing aiki-age and aiki-sage, he is in solid contact with the ground.
Pushing into/engaging with the ground is an initiating step for generating force -- one of the precursors to transforming force into power at the tandan/meimon. Shioda's "sinking of the big toe into the ground" (really, pressing against the ground and gripping with the toes to exploit gravity force and to create torsion), is an example of that starting point for the force-generation process.
Being "rooted" doesn't mean being glued to the ground; mobility is essential to good martial-aikido movement. Someone with a reasonable degree of skill can exploit even just a quick "ground grab" to gain the necessary force for power generation, before moving on. I'd wager that whenever Shioda came to rest -- however briefly -- at any point between stepping and/or propelling himself around, he regained his root to initiate transmission of force.
Plenty of skips and hops here, plus a two-footed leaping slam-dunk:
(BTW, this clip has the classic segment of US Sen. Robert Kennedy and his wife enjoying a private demo with Shioda, with one of the senator's Secret Service bodyguards cheerfully getting himself face-planted.)