The Classical usually transposes to the Scheveningen formation no?, probably less so to the Dragon. If you play the 2...Nc6 move order, 6.Bg5 is good. If you play the Scheveningen move order then 6.Bg5 is not so good, after 6...Be7. but then you have to be prepared to face the Keres Attack with 6.g4 I would rather face the Keres attack in the Scheveningen than the Richter-Rauzer in the Classical. But all of this is moot if you play 2...e6, then you can play the Kan or the Taimanov, and also play the Scheveningen if you are up to facing the Keres Attack. And you will never have to worry about 6.Bg5 again.
After 1. e4 c5 2. Nf3 d6 3. d4 cxd 4. Nxd Nc6 5. Be2 black can play e6 like you describe and it's an interesting game. But black can also play e5 which gives a hole on d5 but also very active piece play. I've played both and have done better with e6 but enjoyed the game more after e5 - dont know why.
As for Keres or Rauzer, the doubled pawn Rauzer structure is pretty specialized but most classical players have studied it in depth so would likely refer it to the Keres attack-- regardless of which is a pawn fraction better. It's just what you understand.
Bill
The Classical usually transposes to the Scheveningen formation no?, probably less so to the Dragon. If you play the 2...Nc6 move order, 6.Bg5 is good. If you play the Scheveningen move order then 6.Bg5 is not so good, after 6...Be7. but then you have to be prepared to face the Keres Attack with 6.g4 I would rather face the Keres attack in the Scheveningen than the Richter-Rauzer in the Classical. But all of this is moot if you play 2...e6, then you can play the Kan or the Taimanov, and also play the Scheveningen if you are up to facing the Keres Attack. And you will never have to worry about 6.Bg5 again.
I had a book on the Classical once. The author claimed Classical only had independant significance if Black played 6...e5 after 6.Be2, or something very much like that.
edit: perhaps should read: if you play ...Nc6 before e6 it's the Richter-Rauzer you have to face. ...Nc6 after ,...e6 the Keres. And if you don't see the Keres, then you will get your Classicl/Schev formation, knights of f6 and c6, pawns on e6 and d6, under circumstances other than the Richter Rauzer.