I dont have 100s of web sites with a password to start with.
What, no on-line banking? No Amazon account, where they have your credit card? Other on-line shopping vendors? Or Credit card accounts? No Netflix? No Flickr? No Facebook? No saving your WiFi password? No 401k/IRA accounts? No mail accounts? Medical account via work? ISP password? Cellular Carrier Password? Cable TV (unless they are also your ISP)? Utilities (Gas/Electric/Water) accounts?
Second, many webpages require a password but have nothing serious going on (eg forums). You can see it all also without password. So why not reuse the password?
That is a habit that can be hard to break, and can come back to bite you. But it is your information and on-line reputation that you are risking.
Anyway, stopping keychain completely is safer for me. I did not yet see how to do it.
I can break keychain (disable all its rights) but it still keeps nagging. Can I block it completely, including its nagging?
I do not know how. It is an integrated part of OS X. Everything requiring authentication feeds through the keychain library services.
You can switch operating systems. You Mac hardware will run Windows and Linux operating systems. Not sure what Windows does for password maintenance, but Linux does not have a built in password manager, so it will definitely not bug you about opening a password manager service.