I don't think Mozilla sites have special techniques to access all files on your computer. That might have been a typo.

Here are some examples of elevated privileges that Mozilla pages have, and which add-ons therefore are blocked from manipulating:

(1) Support site

This site gives the option to extract configuration data from your Firefox including your add-ons and selected preferences. Normal websites are not allowed to access this data. Beyond using it to identify/fingerprint you, I don't know if there are other risks.

(2) Add-ons site

The Add-ons site can extract your extensions list and allowing enabling disabled ones or removing enabled ones (you'll notice this when the button changes on the page for an installed add-on). Normal websites are not allowed to access this data or make such changes. I don't know what else the site allows.

(Probably the Firefox Account site would be very risky to expose to add-ons, but I haven't looked into what it does.)

Why does Mozilla need to access all files? Can we disable this 'feature'?

Examples of what you're talking about would help your case.

See https://support.mozilla.org/hsb/questions/1306789

Only remove the domains you wish to remove.