Are AlphaZero's openings objectively better than the others? If so, why haven't top grandmasters like Carlsen exclusively adopted them in their own games?
Are AlphaZero's openings objectively better than the others?
Not easy to answer. I try: You can not say the openings are "objectively" better because you can not compare openings really "objectively" since chess is not "solved". But you can compare the situations after the opening. which player has a better position after the opening etc.? (Admitted: This is obviously also not 100% objectively answerable, but you can analyse it anyway.)
If that is not enough for you you can compare the entire game results (but then you lose focus on the openings unfortunately): AlphaZero can play chess very very well. So all in all (opening + middlegame + endgame) you can probably say AlphaZero can play better than many other chess-engines. This is a strong clue that also the openings of AlphaZero are slightly better.
Why haven't top grandmasters like Carlsen exclusively adopted them in their own games?
Because it is not enough to memorize an opening from an chess engine. You must really understand the openings from AlphaZero if you want to adopt them in your own games.
It worth nothing when you play a "perfect opening" (adopted from AlphaZero) and then your opponent does one unexpected move and then you do not know how to continue playing and you do not know which move AlphaZero would prefer in this new situation.
I guess they suit more his style, he plays open position and he's not afraid of sacrificing material for activity because he has better assessment when it comes to sharp open positions. However some openings like This French Defense Classical variation with 6. h4 proved to be very hard for A0 because it's already in defense mode and for black (in the game above) to achieve equality he should defend fiercely and precisely for quite some time.
My take on this is that every player uses openings that suits best his playing style, some goes for open games because they feel more comfortable with piece activity and the variety of options (A0 style), others with closed games that need a strong defense technique (like some games of Stockfish A0 follows his gut but it didn't work out)