Qd8 is sound. It is no less sound than Qa5 or Qd6. You cannot punish it. On d8 the queen is safer than on a5 or d6.
https://www.chessgames.com/perl/chessgame?gid=1768345
How to Punish Qd8 in the Scandinavian

Qd8 is sound. It is no less sound than Qa5 or Qd6. You cannot punish it. On d8 the queen is safer than on a5 or d6.
https://www.chessgames.com/perl/chessgame?gid=1768345
Has Qd8 been played in Correspondence Chess where engine assistance is allowed?
@5
In top ICCF correspondence no black players are willing to play the Scandinavian.
Also the Caro-Kann is practically extinct now, mainly because of the Advance Variation.
Even the French is rare.
They have to suffer for 2 years in a passive position to hold the draw.
They all play 1...e5 or 1...c5 now.

So Scandinavian and defense other than e5 and c5 are no longer strong Theoretically. Professional Chess has to reduce Classical Time Control to see variety of chess openings. I propose 60/ 30 time control for classical chess.
@7
In over the board human chess French and Caro-Kann and Scandinavian are still viable.
Correspondence chess however is of much higher level: 5 days/move instead of 3 minutes/move.
@9
"Against players over 2650, what defenses are no longer playable? Owen? Pirc? Philidor?"
++ It depends. As a surprise all of these might be playable. Remember this game:
https://www.chessgames.com/perl/chessgame?gid=1068157
However, regularly playing in high level tournaments, or playing in a World Championship Match is different. It was a surprise Ding played the French in his World Championship Match:
https://www.chessgames.com/perl/chessgame?gid=2479640
Kramnik commented: it is the French, it is OK, it is not Alékhine Defense.
Fischer as a surprise played both Alékhine Defense and Pirc against Spassky in 1972.
Korchnoi played Pirc twice in his match against Karpov
https://www.chessgames.com/perl/chessgame?gid=1068052
'Any opening is good enough, if its reputation is bad enough' - Tartakower

I know I'm U2000 to worry about Dubious Defense. I know White can afford to make a small mistake. For Black it could cost the game. Owens Defense and Philidor Defense is never used by a strong GM in my memory.

The choice of the Center Counter game is already unambitious by black. Look to punish the choice of defense itself instead of the wholly playable 3...Qd8.
@11
"Owens Defense and Philidor Defense is never used by a strong GM"
++ In rapid and blitz strong GM play those regularly.
"I know White can afford to make a small mistake"
++ Black can afford to lose a tempo, white can afford to lose 2 tempi.

There is a fairly recent idea (8.g4!?) which casts doubt on Black's setup (at the cost of a rather poisoned pawn). There is not much theory on it yet, but it seems very dangerous. It is what Super GM Giri suggests in his Chessable 1.e4 repertoire course.
Hint: Don't attempt to practice it without analyzing first!
I know SGMs play 3... Qd8. But if a U2000 play it, looks waste of tempo. How can we punish this unambitious play by black