I'm pretty sure that's how it worked in 4.
Not really.
Most enemies that can be Snatched will lie face down before you, giving you the advantage of attacking without any resistance until the enemy stands up.
This includes all the Scarecrow types, Assaults and Frosts.
Even if they have different body types, such as the bug-like appearances of the Mephisto and Faust or even the Gladius's sword form, they still kinda "lie" down before you after a standing Snatch.
On the other hand, enemies of DmC & DMC5 will stand up after being Pulled/Snatched, even if they were reeled in from a prone position.
This means enemies like Riot can hit you back while tanking your attacks or Scudo Angelos can resume blocking with their shields.
If you knocked down flying enemies like the Pyrobat or Baphomet, you'll have them go back to hovering after you Snatch them.
This also applies to Rawhide's "powered" Snatch, where even "heavy" enemies like the Proto Angelo can be pulled in.
But it seems like putting you in a disadvantage to have it stand up again right after you knocked it down, since it can resume blocking and countering you.
The safest way to Pull/Snatch an enemy in DmC & DMC5 is to do it while in mid-air.
Vergil in general gets a lot of stuff from DmC, from a gameplay perspective.
Even the move Rising Star was originally an Angel mode attack that was passed to Vergil as of DMC4:SE.
As mentioned, inclusion of Doppelganger surprised me the most.