Is there any obvious disadvantage of not castling in a game? The opponent has the option of castling but can I still play a solid game without castling either side? I won some games in bullet time controls but only because position was too complex and opponent lost on time. Please answer with respect to different time controls. (my rating: ~1700 on lichess)
The purpose of castling is to make the king safe. How important castling is in any particular game depends almost entirely on how safe the king is in the center. If the center is completely open (say all four central pawns have been exchanged) and many pieces are still on the board then it is very dangerous to leave the king in the center. If the center is completely closed, however, then the king may be much safer in the center.
On the other hand there are openings (Berlin Defence to the Ruy Lopez for example) where the queens come off very quickly and one side having an uncastled king is fine and confers no disadvantage.
Time controls have nothing to do with this. Having an unsafe king while your opponent's king is safe just makes your opponent's game much easier regardless of time control. You could even argue that the shorter the time control the less time you have to make plans so the easier it is for the player with the safe king because all they have to do is attack the opponent's unsafe king.