As far as my research on this topic has taken me, I agree that that the arima/Arima functions from the stats and forecast packages, does fit transfer functions as you mention, but instead a linear model with ARMA errors.

I don't see the possibility to tell the TSA::arimax function that the $\nu(B)$ should be equal to $\phi(B)$. But you can force the order of all the individual polynomial in $B$ to be what you want, including $0$. But that does not really give you your ARMAX model.

The last thing I can suggest is to take a look at the MARIMA package. It should somehow be able to fit an ARMAX model, but I am not 100 % sure about the procedure.

As far as my research on this topic has taken me, I agree that that the arima/Arima functions from the stats and forecast packages do not fit transfer functions as you mention, but instead a linear model with ARMA errors.

I don't see the possibility to tell the TSA::arimax function that the $\nu(B)$ should be equal to $\phi(B)$. But you can force the order of all the individual polynomial in $B$ to be what you want, including $0$. But that does not really give you your ARMAX model.

The last thing I can suggest is to take a look at the MARIMA package. It should somehow be able to fit an ARMAX model, but I am not 100 % sure about the procedure.