But it's just as easy and just as safe to allow two schemas to co-exist within the same database. If you follow the necessary steps for a risk-free data migration, having both schemas coexist simultaneously and doing gradual switchovers, both models are going to be comparably difficult.
What schemaless lets you do is hide your risk better by disguising those steps. "db.table.update({$set: ...}, {multi: true})" looks friendly, but it's the same terrifying operation as running DROP TABLE A the instant you're done generating table B. And it looks easier, but that's because your code's beliefs about which schema it's reading from are hidden and implicit.