There are weaknesses and attack vectors, but they are in my opinion more secure than almost all realistic alternatives. If you think you’ve come up with a better system, by all means, implement it. I commend your skepticism of following the herd and may it serve you well. But beware of pursuing security through obscurity. People recommend password managers because they are one of the best solutions available for navigating this complex threat environment we live in and they are appropriate for most people’s situations.