It doesn't have to be a black box. There are open source password managers. Bitwarden and Keepassxc are two very good ones.
And keep in mind that even if you can create a reasonably strong algorithm which will both be memorable and resistant to reverse engineering, most people won't. Password managers aren't just good for professionals, they're leagues ahead of anything "mere mortals" use. My mom uses 1password -- that's not a slight, I mean that literally; I put her on my family plan.
I’m in support of password managers if they promote better security hygiene for the average user. Particularly, preventing the most heinous of all password crimes: reuse.
I use an open source password manager, but in the end, I still "trust a black box". I never looked into the source code in detail, nor would I have the knowledge to find some vulnerabilities that later can be used to expose my passwords. It might not be a black box for you, but for all intents and purposes it is for me.
And keep in mind that even if you can create a reasonably strong algorithm which will both be memorable and resistant to reverse engineering, most people won't. Password managers aren't just good for professionals, they're leagues ahead of anything "mere mortals" use. My mom uses 1password -- that's not a slight, I mean that literally; I put her on my family plan.