Fernandinho also never played DM until he got to Manchester City – I watched him every week for Shakhtar and he was more of an attacking playmaker and at times played as a straight-up AM. Then he came to England as a more mature player and the coaches gradually started moving him deeper. Wijnaldum is going through the same transition, as Klopp is moving him ever deeper into midfield and this pre-season is already experimenting with him as the deepest-lying midfielder. BTW Gini already did play as a DM for the National team, for instance at the World Cup against Costa Rica:
Same for Yaya Toure – he was not a DM when he came to Barcelona, he
became one at Barca. Viera was never a DM, he was the definition of a box-to-box player while Petit and Ray Parlour were the defensive specialists in those great Arsenal teams.
Depending on who you ask, a DM might mean this kind of versatile multi-talented player who in the mature stage of their career moves deeper into midfield – Schweinsteiger or Arteta are classic examples – or it can mean a player with severely limited attacking skills who is more like a 5th centre-back playing in midfield: Nigel De Jong, Mascherano, Javi Martinez, Obi Mikel, Lucas etc. If your definition is the 2nd one, then actually not many teams nowadays employ such players with any regularity (see Fernando at Man City who plays only occasionally) and actually the current trend is to convert such players to CB. If your definition is the first one, then Can, Hendo and increasingly even Wijnaldum fit this definition just about as well as any of our rivals' midfielders.
BTW Keita would have not satisfied your desire for a "quality DM" , because he quite obviously belongs to the first (versatile and multi-talented) category.