  In recent years, $f(Q)$ gravity has enjoyed considerable attention in the
literature and important results have been obtained. However, the question of
how many physical degrees of freedom the theory propagates -- and how this
number may depend on the form of the function $f$ -- has not been answered
satisfactorily. In this article we show that a Hamiltonian analysis based on
the Dirac-Bergmann algorithm -- one of the standard methods to address this
type of question -- fails. We isolate the source of the failure, show that
other commonly considered teleparallel theories of gravity are affected by the
same problem, and we point out that the number of degrees of freedom obtained
in Phys. Rev. D 106 no. 4, (2022) by K. Hu, T. Katsuragawa, and T. Qui (namely
eight), based on the Dirac-Bergmann algorithm, is wrong. Using a different
approach, we show that the upper bound on the degrees of freedom is seven.
Finally, we propose a more promising strategy for settling this important
question.
