The deisgn illustrated would have no advantages for speed at all.

On a bicycle, if you can increase the power input, you can ride a
higher gear at a given cadence, and therefore go faster.

Power is not the issue on a unicycle. Turning a 20 - 36 inch wheel is
not difficult and does not require a lot of torque at all. The problem
is simply one of coordination. How fast can you spin the wheel whilst
maintaining control? You can improve this by selecting an appropriate
length of cranks (short cranks = potentially faster, but at the expense
of some control) and by practising!

As I understand your diagram, the hands and feet are each contributing
driving force to the wheel, and are connected by a chain. I assume a
1:1 ratio between hands and feet. Anything other than that would be
very difficult to co-ordinate, allthough I guess 2:1 would not be
impossible.

So you are increasing the torque available, but not the rpm. In fact,
because of the additional co-ordination problem of having hands as well
as feet pumping away, you are probably losing rpm.

So you need to gear up the hub. Lots of people have experimented with
geared hubs. It is possible to gear up the rotation of the wheel to
about 1.6 or 1.7 (approx.) times the rotation of the cranks. Even that
is the equivalent of a very low gear on a bicycle.

At best you have a very pretty picture of something that would be more
difficult to ride, and much harder to steer than a conventiojnal
unicycle; which would if anything be slower on the flat, and a fair bit
more dangerous. The only advantage I can see - and that a theoretical
one only - is that it might be good for hillclimbing, on smooth
straight steep hills.


--
Mikefule

"The world is Hell, and men are on the one hand the tormented souls, and
on the other the devils in it."
Arthur "Cheery" Schopenhauer
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