When should <script> tags be visible and why can they?

The HTML5 specification defines a style sheet that user agents (like browsers) are expected to use. Section 10.3.1 lists the styles for "Hidden elements":

@namespace url(http://www.w3.org/1999/xhtml);

[hidden], area, base, basefont, datalist, head, link,
meta, noembed, noframes, param, rp, script, source, style, template, track, title {
  display: none;
}

embed[hidden] { display: inline; height: 0; width: 0; }

As you can see, it applies display: none; to script.

This is the only "barrier" between your users and hidden script elements. It’s perfectly fine and intended to be able to overwrite styles from user-agent style sheets within author style sheets (and of course also within user style sheets).

Why someone might want to use it? One use case is displaying content without having to escape characters like </>, similar to the old xmp element. The script element can be used not only for scripts, but also for data blocks (i.e., for anything with a MIME type).

Why can <script> Tags be visible?

Because they are HTML elements like any other and there is no reason to write special case rules in the HTML specification (which would add complexity) to prevent CSS from applying to them.

Any element can be styled. Take, for example:

head { display: block; }
title { display: block; }
meta { display: block; }
meta[charset]:after { display: block; content: attr(charset); }
meta[content]:after { display: block; content: attr(content); }

Is there any Usecase where it is wanted?

Certainly no common ones, but general rules aren't designed to make sense for everything that you can apply them to. They are designed for the common cases.