Arguments against a systematic development of thread algebra can be easily formulated. Of course there is little point in raising objections to the development of a theory of thread algebra as such, but the viewpoint that the resulting theory bears on its intended applications can be criticized. Now TA may be criticized on the following grounds:
TA axiom systems are ad hoc and sometimes hard to read, the theory lacks elegance.
The focus on a single strategy, or on a limited set of strategies denies the need for the development of suitable abstractions. One needs abstractions from strategies admitting quantification over a large and natural class of strategies.
Cyclic interleaving is too simple to be valid in any application. In particular if networks are nested (hierarchical) cyclic interleaving is considered an unreasonable assumption.
Verifications based on one or just a few strategies have no practical value.
The underlying model of a thread, inherited from program algebra is too simple.