As you pointed out, this task is already processed by Doctrine tools.
The reason why Skipper doesn't do this task is that each ORM framework handles database structure on its own. Also advanced features like inheritance, collection, embedded etc. is ORM framework dependent and can vary based on feature configuration (for example based on inheritance type there are several ways how data are stored in database).
So we would have to implement the whole and complete logic already implemented by each ORM framework independently to be able to implement database export.
From the reasons described above currently we are not considering this feature. Maybe in the future we will implement some standalone plugin for this but currently we don't have specific date.
PS: Maybe you can use some third-party tool or migrations to distribute database changes to production.