What I think are the dangers of using 3rd party Wallets:

1. Access - Because the website is freely accessible online on any browsers, your personal information namely your wallet address could be in trouble. If you are outside and are using a public network then you are more vulnerable to cyber attacks.

2. Security - 3rd party wallets need to safely protect your information from prying eyes, they may have very weak encryption and hackers might be able to breach, also their admins and staff could also circumvent their own security and this may lead to you losing all your money on your wallet when that employee decides to go rogue.

My 2 cents. Thanks!