After T164898, only Oracle will require Database::nextSequenceValue() to be called prior to inserting a row into a table with an auto-increment column. I propose emulating MySQL's behaviour in a trigger. The trigger could store the sequence name or value somewhere so that it can be retrieved in insertId() without the caller having to know the sequence name. Or Database::insert() could store the last-used table name, and trigger names could be derivable from table names. Then the CURRVAL pseudocolumn could be used.
Then Database::nextSequenceValue() can be deprecated. There will be no remaining references to sequences and sequence names except as implementation details hidden inside Database subclasses.