For us (with a much younger DD almost 8), the social component has been important all along. One of the reasons we wanted a grade skip (as opposed to either subject acceleration or staying where she was) was for social reasons.
DD has end-of-school-itis, which expresses itself in complaints about her current school situation, so I'm at least giving brief consideration to the alternatives. For us right now, "doesn't exacerbate a weakness" gets more weight than "enhances a strength." DD is the kind of kid who needs an early bedtime and unstructured time to unwind, plus she's not a fast worker. The private schools that have 1-3 hours of mandatory homework a night (compared to the 30 minutes of suggested, but not mandatory, math / reading / spelling practice our public school asks for), on top of a 45-minutes-each-way commute (compared to a 10-minute-each-way commute to public) would grind her down. So they're off the list, even though they have some really great opportunities to keep her with age peers while working on advanced stuff.