Ironically it might increase privacy for naive users, as they won't make the mistake of making sensitive Monero transactions using an online exchange wallet.
Send money from the exchange to a local anonymous wallet (like the official one [0]), and then use that wallet for private stuff.
Most people who offer XMR/FIAT exchanges (like localmonero.co) are trading on exchanges like Binance in the background, and sell it to you (privacy focused, anonymous user) with an additional commission.
Such traders aren't concerned about a "government identity being tied to an exchange wallet" and whatnot. They just want to make money, and liquidity is important for a currency.