Read this proposal re lower gas fees
TL;DR: Centralized Exchanges do two tx instead of one; some form of specifying into which account funds should flow would cut this in half. Memos are one idea, EIP-2876, and EIP-3074 which is being considered for London in summer would also help, though not as much as memos EIP-2876 style.
1559: Not likely to greatly reduce gas fees.
L2: Very likely to help. Doesn't help the CEX thing, but still helps.