[musgravepeter]

My perception (as a lapsed PhD physicist) is the community takes on a new formalism when it has to i.e. there are new results that can only be derived with the new formalism. A formalism that allows slightly better derivation of existing results does not attract attention. Twistors, Clifford algebras and other things seem to have not met this hurdle so far.

Feynman diagrams, Riemannian geometry (General Relativity) did.

[filmor]

Clifford algebras are used whenever you use Gamma matrices, I think their a well established.

[eigenspace]

I think the person you're replying to was talking about Geometric Algebra, which is more of a project to reformulate all our current vector and tensor notation in terms of Clifford algebras and to move away from using specific representations of the algebra and instead just leverage the algebraic properties themselves.

If you look at how most physicists use the gamma matrices, they are very reluctant to treat them as algebraic objects and rely heavily on their matrix representation. A proponent of GA would say this is like using the matrix

    [ 0 1
    [-1 0]

everywhere in your calculations instead of just using i and remembering that i^2 = -1. Sure, it's formally equivalent but you'd still miss out on a lot of the beauty of the complex numbers.

For what it's worth, I have a soft spot in my heart from Geometric Algebra, but I think it still needs a lot of notational improvement before it'll ever see any real adoption.

If you're curious about GA as it currently stands, I'd check out Geometric Algebra for Physicists by Doran and Lasenby.