I timed it and it took about 25 seconds to go from the Chase login prompt to the "Add authorized user" page where you can get another credit card added to an existing account. So, I admit its not quite as fast as you would like. There is a caveat if you pay an annual fee: you pay the fee for each card. My accounts have no annual fee.
I also checked US Bank and American Express and you are correct, the process is not smooth at all. US Bank wants me to print, sign, and mail it! American Express wants to verify identity of the additional user using an SSN. That makes no sense of course, because they might not even have an SSN and the main account holder is still contractually obliged to pay the account balance.