This is a follow-up to the following answer: https://mathoverflow.net/questions/4379/solvable-class-field-theory/4386#4386 in which it is stated as a "folklore" conjecture that the maximal solvable extension of Q is pseudo algebraically closed (this means, in particular, any geometrically connected variety over Q has a point over a solvable extension). I am curious what evidence there is to support such a conjecture. In addition, what can be said for the analogous statement for global function fields?