I don't understand what this has to do with strict mode? Yes those types should exist, but the workaround is to use an integer column for bool and a text column for date, whether or not you're using strict mode.
The point of strict mode is that the RDBMS performs data type validation when inserting/updating data. If you use a text column for storing dates, you can store any string in the column, not just valid dates. That's not strict.