Why is that the ideal? With SQLite your database is 1:1 connected to your application (meaning there is no other application using that database), it doesn't make sense to move the app to a new version but not the database or vice versa. Running migrations on startup of the app is ideal.
Migrations are a bit more difficult to write for SQLite than they need to be (DROP column only being added recently...), though. I usually iterate a few times to get the column definitions just right so that I don't have to change them later.
As you say column types are limited (and enforcement lax) but in practice it's a non-issue because you convert the data to application-specific types when reading from db (and enforce by writing only right data types) anyway.