The solvable monodromy extension property and varieties of log general type

We speculate on the relationship between the solvable monodromy extension (SME) property and log canonical models. A motivating example is the moduli space of smooth curves which, by earlier work, is known to have this SME property. In this case the maximal SME compactification is the moduli space of stable nodal curves which coincides with its log canonical model.