This is because, in the restaurant's view, the menu is a marketing tool that should influence customers to order items for profitability. Dollar signs can obstruct that goal.
The visual repetition of dollar signs all over a menu can remind customers that they’re about to spend money, potentially discouraging them from ordering a more expensive item.
Without dollar signs, the communication of price is more subtle. Hypothetically, it keeps customers focused on browsing the offerings, rather than their cost.
The lack of dollar signs isn’t the only way restaurants influence customers. Everything from the font on the menu to the layout can influence how diners spend their money.