clifford's algebra bottle neck in one page,
the bottleneck isn't the base tool (binary/geometric prod) it's that generality at scale costs you search/address overhead, same as extra basis components cost you compute.
[explained the bottleneck in thread,do check]
it multiplies work, because componets gets doubled(2^n) as each domain adds up. So bivector solves the problem with cross product but it increases these factors.(mainly compute)
I am still sharpening my axes more on this.
Clifford alg introduced bivector (because cross product wasn't representing the patch bw vectors,instead it was introducing another perpendicular vector). But , incase of bivector , as number of domain gets added up ,there is an exponential increase in cost of storage and