On the web page of the Error Correction Zoo for the [[7,1,3]] Steane Code, there are quite a few realizations on trapped-ion devices. In fact, there are a lot of implementations generally compared to other devices. For me, this seems like hardware research slightly tilts towards the Steane code.
Does the Steane Code have characteristics that make it especially useful for trapped-ion devices? And could a possible reason be the transversal implementation of the Clifford gates?