Do Self-Aggregation Simulations Depend Crucially on Radiative-Convective Equilibrium (RCE) Initial Conditions?

I’ve been reading papers on convective self-aggregation, such as Bretherton (2005) and Khairoutdinov (2003), and it’s not clear to me why (or whether) self-aggregation depends on the model being initialised from radiative convective equilibrium (RCE). Are there any papers that show self-aggregation can occur in homogenous, no-shear, non-RCE conditions?

It’s possible I’m missing the point of these studies. It may be the idea is more that it’s surprising aggregation occurs despite RCE, because RCE is supposed to represent a balanced equilibrium state. Would this mean aggregation disrupts RCE, and that RCE is actually an "unstable" equilibrium?