I would like to see the "migrate" option disappear, for multiple reasons.
First, it seems presumptuous for those of us who don't participate on, say, math.stackexchange, to express opinions about what's appropriate there --- let alone to actually cause things to be posted there.
Second, it makes life just a little easier for those who posted inappropriately to MO in the first place, and therefore makes it just a little more likely that they'll do it again. It used to be that the cost of having your MSE-appropriate question closed on MO was that you'd have to go to MSE and type it in again. Now you can just wait for someone to migrate it for you, so there's that much more temptation to "take a shot" at MO and see what happens.
I of course have no actual data on whether the "migrate" option draws more marginal questions to MO, but it seems quite plausible that it does, and that the effect will grow over time.
Third, the "migrated" questions continue to appear on the MO questions list --- albeit marked "migrated" --- and I'm not sure whether they ever disappear. This makes them almost as distracting as if they'd never been migrated away in the first place.
These costs might be small, but I see no offsetting benefits so (unless there are benefits I'm not seeing) we'd be better off without this feature.