Sure enough, taking a page at random, we can quickly find MySQL-specific SQL being issued through the "abstraction" layer:
// get the subset (based on limits) of required records
$query = "SELECT cd.*, cc.title AS category, u.name AS user, v.name as editor"
. "\n FROM #__contact_details AS cd"
. "\n LEFT JOIN #__categories AS cc ON cc.id = cd.catid"
. "\n LEFT JOIN #__users AS u ON u.id = cd.user_id"
. "\n LEFT JOIN #__users AS v ON v.id = cd.checked_out"
. $where
. "\n ORDER BY cd.catid, cd.ordering, cd.name ASC"
. "\n LIMIT $pageNav->limitstart, $pageNav->limit"
;
$database->setQuery( $query );
$rows = $database->loadObjectList();
So there are some problems here from a portability perspective, primarily in the hard-coded non-standard LIMIT clause. It is not worth defining a database abstraction layer for your application if you are going to issue SQL directly from within every other file in your application.
Instead, consider defining a database abstraction with functions, or classes and methods, for the functionality required by your application, so that other databases can simply implement that interface. Then a simple setting in the user's configuration file will determine which database they want to use, and which implementation of the application logic to invoke.
For example, instead of defining Myappdb::issueQuery(), define Myapp::getActiveEditors() with the expected input parameters and expected return values, and let the actual database-specific code implement that in the most efficient way.