In short, I'm trying to build a high-torque and high-RPM robotic arm, and I think brushless motors are the best compromise. The motors I'm considering are 400KV, and are supposed to run on 6S. Are there any glaring errors with my idea?
You will have some losses in torque due to fiction and the elastic deformation needed for the cycloidal drive.
Your math, other then losses, is fine, but you have to consider also the technological parameters. You have to make sure that the gearbox supports 10.000 rpm (it might overheat if it was designed as a lower speed gearbox) and that it is rated for the torque input and output (the internal components and gears might get damaged if you are over the rated torque). Furthermore, there is more to a gearbox, then just axial load and rpm. You have to make sure that the radial loads on the gearbox are also in spec, otherwise you might snap the shaft off or damage the bearings.
As far as I know, current large scale industrial robots, use even higher gearbox ratios.
You need to consider both the max rated input speed of the drive (as another answer suggests) as well as the rated torque of the cycloidal drive.
The rated torque is the torque at which the drive can operate for some number of input cycles - typically 1 billion. Reducers (aka gearboxes or drives or transmissions) also have peak and max input torque ratings as well.
The speed may be the killer here, though. If you check out the specs of the Nabtesco RV-N series, for example, the allowable output speed is only 100 rpm or so (i.e. 5000 rpm input).
10000 rpm is really high, I think. Speeds of 1000 rpm or less are more typical I believe.