But it turns out that keeping that 1 login and password in your head and trusting the rest to your password service (especially if you let it make random passwords) is way more secure than what people do if they have to try to keep them all in their head.
So it's about relative security. Both sides are correct, in their narrow views of the situation.
But it depends on your threat model and attack surface area/shape. A strong password on a post-it on your monitor is stupidly insecure locally, but far more than just having a weak password if you consider only non-local (to the user) attacks (neither that site hacker in far-off Hackyoustan nor his pet bots can see the post-it, but could try brute force a short easy to remember password).