Deterministic code cannot receive a side channel. It may, as you point out, be able to transmit on a side channel. It might even be able to "reflect" one side

Deterministic code cannot receive a side channel. It may, as you point out, be able to transmit on a side channel. It might even be able to "reflect" one side channel into another one. But these risks seem both less severe and more easily mitigated. At least, the history of attacks of the latter types is not very impressive.