It's almost like DmC had some good ideas despite some dumbness here and there. lol
Actually, I'd argue both of those ideas weren't that good. Doppelganger as a boss fight mechanic borders into the kind of boss design that spawns minions to unleash on you, which I find cheap design and kind of annoying. It's best left as a mechanic for the player.
And the sword embed was just the worst thing they could have taken from DmC Vergil. It made the teleport slower and clunkier to use, especially from a distance. In 4, you now had to wait for the sword to reach the enemy before you're allowed to teleport. Compare that to how his Trick moves were in DMC3. Instantaneous, you input the command and he teleports. In 4SE, it can even happen that the sword gets blocked by some geometry or object (the start of mission 2, near the fountain, is a prime example of where this can occur, ugh), and in that case you can't teleport at all. They should have left the Trick mechanic as it was in DMC3SE, and the sword embed should have been something not tied to teleport, but more of a purely offensive kind of deal, cause the mechanic where you stick some into an enemy and they explode when Vergil sheathes Yamato is pretty cool.
DmC did have some good ideas that were ported over to DMC, like free camera, training mode and trying moves before you buy them (DmC had that, if I ain't mistaken), but the ones mentioned earlier for Vergil aren't it, imo.