In my opinion, the article is very mistitled, because it does not contain even a single valid criticism against the geometric algebra theory, despite containing some perfectly valid criticism against some mistakes frequently made by geometric algebra proponents.

The author has completely failed to understand the meaning and the purpose of geometric algebras, though to be fair this is not entirely the author's fault, because there are a lot of bad presentations of the geometric algebra theory, many of which contain actual mathematical mistakes, as listed in an article by Eric Lengyel that is linked in the parent article.

The main correct criticism of the parent article is that the geometric product is an operation that is seldom useful in practice.

In practice, the important operations are the generalizations of the inner product and of the outer product. The inner product and the outer product have been defined by Hermann Grassmann in the 19th century and the publications of Grassmann together with the theory of quaternions by Hamilton have been the sources on which William Kingdon Clifford has created the theory of geometric algebras.

Unfortunately, today a lot of people use incorrectly the term "outer product", using it to name the product defined by Johann Georg Zehfuss, which is also called "tensor product". "Tensor product" is also not a really appropriate term, but at least it is not as ambiguous as "outer product" has become, so it should always be preferred for the Zehfuss product. For the outer product in the Grassmann sense, a non-ambiguous term is "wedge product" though it is rather meaningless.

While the geometric product does not have a practical importance, it has a great theoretical importance, because with it the geometric algebras can be defined with a small set of simple and natural axioms. Then the operations that are important in practice, i.e. the generalized inner and outer (wedge) products can be defined based on the geometric product.

The author is right that some geometric algebra proponents have tried to shoehorn the use of the geometric product in some applications for which it is not the right tool, but that has nothing to do with the theory of geometric algebras.

The theory of geometric algebras has a modest practical importance, but it has an immense theoretical importance, because it unifies many mathematical concepts that previously seemed to be unrelated and it illuminates the relationships between them and also the distinctions between things that were previously confused, even by the best mathematicians and physicists, for more than a century.

There is a high probability that the progress of physics has been delayed by many decades by the fact that both William Clifford and James Clerk Maxwell have died prematurely and almost simultaneously, before they could make order, based on the theory of geometric algebras, in the mess that was at that time the theory of vectors, complex numbers and quaternions. After their death, the theory of geometric algebras has been forgotten and a lot of mistaken theories of vectors have been created, by Josiah Willard Gibbs, Oliver Heaviside and others (because they did not understand the relationships between various physical quantities, like polar vectors, axial vectors, quaternions, complex numbers, pseudoscalars).

When I have first encountered the theory of geometric algebras, that was one of the most beautiful moments in my experience of learning mathematics, it was like turning the light on in a dark room full of previously hidden things. The only similar moments, have been when learning for the first time projective geometry, the theory of spatial symmetry groups and certain parts of topology, which are also theories that have unified a great number of seemingly unrelated concepts.

Like I have said, geometric algebras have very little importance for writing algorithms or the like, where the classic linear algebra with matrices is what matters most, but anyone who does not understand geometric algebras does not really understand physics and this lack of understanding will prevent the correct solution of many problems.