Who cares what you call him? Rodgers played Gerrard as the deepest midfielder for a big portion of last season, to do the defending when everyone ahead of him got overrun. You can call it DLPM as much as you want, and Rodgers can call it that too in his 180 page whatever. But when the smoke clears, he played him as a DM, to shield the back line.
No, he isn't there to "shield the back line" that's the point.
That's why he's not a "DM". It's an entirely different role within the formation not just calling someone by a different label.
It's like calling Allen the striker rather than a central midfielder just because he will take some shots "when the smoke clears and there is noone else in front of him".
As pointed out in my previous post, if you can't appreciate the obvious difference, you won't realise how the rest of the midfield is set up to allow the DLPM to work, let alone how the centre backs and goalkeeper should be playing behind them.
Having a basic understanding of the position is the key to understanding the system. Replace Gerrard, Alonso or Pirlo with a "DM" whose strengths are shielding and tackling in those systems and watch what happens to the team as a whole.
That's the point you are missing. Can might be better defensively but is he ready to consistently run the game and create the play at the heart of the team like those three?
Back to the original point, we could try him in a 14231 alongside Lucas as a "DM" but the results of doing that with Mascherano and Lucas weren't spectacular even when they were the best two DMs in the league, better fullbacks and a goalkeeper who allowed the centre backs to compress the play behind them rather than sticking rigidly to his line.
The entire system is predicated on trying to maximise Gerrard's strengths and negate his weaknesses. Simply swopping him for Can unbalances the whole team even further since they are completely different players.
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