Not only it would be desirable, but it is already implemented elsewhere as in Cadabra [quoted from its site]:

Cadabra is a computer algebra system (CAS) designed specifically for the solution of problems encountered in field theory.

Key features of Cadabra:

• Input and output using TeX notation.
• Designed for field-theory problems, with handling of anti-commuting and non-commuting objects without special notations for their products, gamma matrix algebra, Fierz identities, Dirac conjugation, vielbeine, flat and curved, covariant and contravariant indices, implicit dependence of tensors on coordinates, partial and covariant derivatives...
• Powerful tensor simplification algorithms, not just for mono-term symmetries but also for multi-terms symmetries like the Bianchi identity, or dimensionally-dependent symmetries like the Schouten identity.

In fact, its notebooks are ordinary  LaTeX files (article class) that you can process as usual.