It's the equivalent of sharing your bank account number with scammysitedotcom. Even if there are no security implications, sharing your entire financial history with any website is very privacy hostile.
Not necessarily. You should use a different account (preferably one with 0 transaction history, if no on-chain txes are needed) than your main financial account (and really, anyone not living paycheck to paycheck should have more than one of those in the first place. Cold/hot, have a separate one for any defi activities, use a new one for each L2, etc)
Just like you may not have the same email for job applications and dodgy e-commerce, or bring all your cash and cards with you in a purse to the nightclub.
(GP did say “shared across sites”, which should be a very deliberate decision and not the default. UX needs to improve to have better privacy by default. I could imagine Metamask defaulting to generating and connecting a unique address for each domain, requiring manually selecting accounts to have them shared)
Based on your comment, I'm guessing you've never used Metamask or similar before. You really should check it out and see just how trivial creating a new wallet is. HD wallets lend themselves to this kind of UX.
