A block-based theme (also called Full-Site Editing theme) is a theme that by definition uses the new site-editor screen to build layouts. In that screen, users have access to global styles where they can define things like background-colors, typography etc for their site, and they can build their layouts as they wish. So it makes sense to hide the links to the customizer & widget screens when such a theme is used.
There are still a couple of things in the customizer that are not yet supported by global-styles, but these will eventually all be added. As for widget areas in an FSE theme, they are no longer necessary. Users can add a group block wherever they want, think of it as a widget-area and add blocks in there for everything their widgets used to previously do.
Want a sidebar next to the content? No problem, just add 2 columns, content on the left and "widgets"/blocks on the right.
Full-Site editing doesn't deprecate anything. It simply abstracts the ideas a bit and allows for greater flexibility. We will essentially have an infinite number of widget-areas, wherever we want them in our layouts. They will no longer be called "widget-areas", they are just content-areas where we can place anything, including widgets.

As for legacy/classic themes, these won't be affected at all. The customizer and widgets will continue working there perfectly fine.