In this scenario you increased your privacy when you withdrew your bitcoins and then mixed them before moving them to your storage device not by deleting your account since when you delete your account it is only removed from the public database you access for loging in, for all we know Binance (and any other centralized exchange with a KYC) is obligated by the government to keep a complete report of all their customers and transactions and be ready to hand it over. Which means your "footprint" is stored somewhere by Binance and in case of a hack it will leak.
That would be my assumption too. Once you give your personal data, it's safe to assume they'll never remove it.
On binance, I can decide to open and account, use it to buy Bitcoin after verification, after I buy the Bitcoin, I can send it to a wallet like electrum, I can decide to delete my Binance account (in which all my data would be deleted along, although, it is what Binance indicated, but I do not know how true it is).
The only way to be sure they don't keep your data, is by not sending it in the first place.
While my Bitcoin is on Electrum, I can make use of mixer/tumbler to mix the Bitcoin and have it finally sent to Trezor wallet. Assuming I am using Tor or VPN to access my noncustodial wallets which makes the connection throught it to be more private.
Who are you trying to hide from? Say Binance gets hacked, a local crook sees you bought Bitcoin, and decides to pay you a visit. How does mixing your coins help you in this scenario? The crook will see your Bitcoin was moved to a new address, and even though you mixed it, he'll just use his $5 wrench until you give up your coins.