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.
I haven't followed Monero in the last years, I had thought it was one of the very few coins harder to track. What would be the optimal way to take the cash out then?
The real killer feature in Monero is privacy by obfuscating transactions. Using an exchange wallet tied to your government identity for private transactions defeats the purpose because a bad actor could access the exchange database, like with a traditional bank account.
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.