I don't think the reason for GEE not to be popular is "software availability/implementation". Almost all software I am aware of and have been working for a while (STATA, R, SPSS) can do GEE. I wonder if there is any software that can do mixed and never(or difficult to do) GEE.
As explained here "Mixed Model Versus GEE estimates and which to use" in a little bit more detail, I don't think it is neither the interpretation that matters.
Even some authors (Hubbard AE et al, 2010) argue mixed model suffers from " unverifiable assumptions on the data-generating distribution".
Literature is full of the idea that "GEE allows robust inference even if a choice of correlation model is wrong or misspecified" and in case of mixed model "SE not robust to model misspecification".
I personally think GEE is computationally exhaustive than mixed; whether in hand or in software, if you do it nice and clean; that may be.