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I didn't mind having mobility a little impaired for a while in Sac Chess,
in terms of available legal move options from the starting position. Humans
might even be able know better than engines for the forseeable future which
pieces to develop faster than much of the rest of the pieces, leaving such
as 'reserves' for a long time into the game. In any case, the average
number of legal moves per turn in a game would still significantly reduce the number
of ply ahead a machine could look, I figured. 

Even a modern off-the-shelf chess engine that prunes moves each turn highly selectively (say
like the engine Houdini) sees 40 ply ahead on average, I seem to recall. In
that case, I've estimated that for Sac Chess such an engine might see only
about 30 ply ahead, and maybe a further 5 ply less than that if any
practical memory use requirements (due to using a larger 10x10 board) also
limit the search depth. If my guesswork was not that far off, that could
make a strong Sac Chess engine only strong international master level
strength at best (e.g. 2450 FIDE). By contrast my guesswork for Grand Chess
puts a strong engine at that at about 2750 FIDE (all this is assuming
Houdini-like prowess of such engines, in terms of evaluating positions). Of
course, something may be wrong with the sort of calculations I made.

Even so, I'd be curious to know how strong an engine might be at Capablanca Chess
(8x10 board variant) - if it's weaker than a strong human than I may have grossly overestimated how good a Grand Chess engine might be, for example. In the case of Seirawan Chess, adding two more pieces
per side in the opening didn't seem to help humans when vs. strong engines, I gather, but that game
is played on the smaller 8x8 board still.

I'm not sure if having two moves per turn could one day make for a popular enough variant. As an analogy, I long ago played some sort of card game where a player could under certain conditions pick up another card from the deck after making a play, thus continuing their turn, and that process could even repeat itself indefinitely. I played that card game with older people (for the first time), introducing them to it, and they never seemed to desire to try it again. It seems there is a strong cultural habit/desire of one person taking one turn at a time, and that's it, at least for card games. To be fair, I liked playing Progressive Chess with a friend who was willing, long ago too.