My point is exactly that the square root function is, in all common usage, distinct from the solve function. If we insist on conflating the two, how do we interpret an expression like \sqrt{2} + \sqrt{3}? It’s got to be a four-element set, I suppose. Here we’re already verging on chaos, wishing we had a concise way to say “the positive square root” when we want to.
I’m comfortable granting the point that there are many interesting loci of interplay between the demands of symbolic and numeric computation, some of which may require creative thinking about how common concepts need to be treated differently. But I remain skeptical about the specific proposal of abandoning the square root function (which is implied by an assertion like \sqrt{9} = \pm 3).