In general, password managers are a must-have in today’s world. The question is not if you should have one, but which one and why.
As a Software Engineer very conscious about security and privacy, but also with a high practicality sense, I’d say you should opt for whatever you feel more comfortable.
If you don’t want to manage anything, then 1password, BitWarden, LastPass or any of those might be right for you. If you are more of the kind to tinker with everything, then you can have your own OwnCloud/NextCloud and use KeePassXC.
I particularly used the later setup, but NextCloud was too much to handle for me, and settled with KeePassXC + Dropbox.
You do you, but use a password manager.
Let’s agree to disagree. It’s true that these companies are vulnerable and lovely honeypots for hackers. And because they know that, they’ll try to harden as much as possible. Besides, not everyone is willing to create passwords out of algorithms seeded with mnemonics. Most of the people will reuse the same password over and over in different places. And that’s the worst situation, because most of those sites are hundreds of times more hackable than commercial password managers.
Are there better options than commercial password managers? Yes, of course. How many are willing to use them? Maybe less than 30% of the population. And that’s bad, because it makes the internet less safe for everyone.
And by the way, the method you use is one of the earliest ways to create passwords and is hackable by brute force in seconds. If I have two or more passwords, or two or more seeds, the algorithm is done unless you have some random generator in it.