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.
But one huge advantage of MongoDB is that it is schemaless. And so you have a lot more options for how you migrate documents. For example you can move all of the data under a particular key e.g. "v1" and allow two schemas to co-exist within the one document. Significantly less risky than running migration scripts or doing a alter schema in production.