Did you know that Chrome saves passwords?

You would be surprised.

A computer networking instructor said to his class one day that the safest computer on Earth is the one that you  bury 20 feet deep below the ground.

He added, dig a hole about 20 feet deep, then lock that computer with chains and combination padlocks.

Then pour in concrete all over it to cover the hole where it was buried... and then cover the sitesome more with another thick layer of dirt and soil... just to make  sure that this computer will never ever be connected to the Internet again.

Don't forget in FireFox you can also check if you have been compromised. To check use something like FireFox Monitor. Works really well.

https://monitor.firefox.com/

++ EDITED REPLY ... fixed some grammar and typos

That is true JR, but let's not forget that installing extensions, add-ons, or plug-ins also make the most secured web browsers prone to leaking.

Most important is, to keep in mind that web browsers with webRTC protocol enabled also leak your DNS queries, and reveal your private network IP addressing.

There's a lot more involved that should be combined with safe online hygiene habits rather than just saving passwords in a centralized secured location.

That said, just like backing up data frequently to the same storage location, Is it a good practice to save passwords centrally in the same directory to begin with?

Is the directory where the browser passwords are saved to properly encrypted? 

If yes, what type of encryption? 

And even if encryption exists, how can we ever be sure that the password manager security vault is not compromised by an attacker or a cyber criminal?

You may also have to spend some extra time in learning how to disable the hidden experimental features that are shipped and activated by default in all modern families of web browsers. 

Most of these hidden features are designed to share with third-parties even more about the user interactions on the web.

I would say to go old school; memorize your own passwords and change them periodically.

While incovenient as this may be, not because a password manager makes it  more secured than a web browser's built-in password manager, and not because an external password manager with encryption makes it easier for a user to stayed signed in in multiple devices or multiple web sites, employing the use of an external password manager doesn't necessarily mean that it won't become compromised at some point.

Just think about it:

One password  giving access to every device and  every online sites that we unlock on a daily basis through our favorite web browser(s)?