Let's say there is a player who knows nothing about Sicilian Defense. If they always start the game with 1. d4 or 1. c4 as white and play the Caro-Kann as black against 1. e4, it seems to me that they can theoretically be a player at the top level without knowing anything about Sicilian. Of course, they will have a problem coaching others, but I do not see why zero knowledge of the Sicilian can prevent them from being a top-level player.
Wilhelm Steinitz: I have never in my life played the French Defence, which is the dullest of all openings.
So you go into your first top-level tournament and get Black in the first round. No problem, you'll just play your Caro-Kann. Play goes 1. e4 c6 2. c4 d5 3. cxd5 cxd5 4. exd5 Qxd5 5. d4. You've just transposed into a line of the Alapin Variation of the Sicilian.
In the second round you're White and play 1.c4. Your opponent plays 1...e5 to go into a reversed Sicilian, and suddenly you're really wishing you knew something about that opening.
No player knows "all" the popular openings. Players have repetoires that include the range of openings that they want to play. Even with fairly complete repetoires it is possible to have to play ad hoc anyway. For example, moves like 1. b4 and 1. g4 (the "Spike") can throw a player out of book right away. Bent Larsen frequently played 1. b3 to avoid book openings.
Some players have very narrow repetoires. This is most often seen with the English opening. Players will learn the English with a King's Indian attack for White side and then the Dutch Defense (1. d4 f5) and Modern Defense (1. e4 d6/g6) as Black and that will cover 95%+ of the possibilities. If someone plays the English against them, then they play the symmetrical variation (1. c4 c5). Since all four of these systems have similar strategies and themes, the player essentially needs to learn only one pattern of play.