Of cos web wallets are bad, vulnerable to attacks from hackers and lose of password and login is very possible, the biggest issue is no private key or recovery seed, once wallet stop working thats it
About security reason, I agree with you. But, about seed or PK on web wallet, I'm not agree, if you are using blockchain.com you are able to get your PK on setting menu. It's different if you are talking about exchange wallet, they will never give you your seed or PK.