Fonts are confusing, and reports of font failures are usually confusing as well - "works for me!" is a common outcome.
The original post is not clear enough (for me) to know what the problem is there - there is a font named Symbol provided by Apple on the Mac. It shows up for me on the font dropdown in the Character Panel. So it is installed and does appear.
A bit later down though, we have a sample usage in After Effects - clearly the font DID appear there as well - but there are blanks in the typing.
The reason for the latter is that the Symbol font does not contain glyphs for roman/latin letters. It does contains number and symbols.
What IS interesting to me is that we get blank glyphs instead of anything else - and that should not be happening.
Usually when the selected font does not have a glyph for a typed character, and silent fallback occurs to a different font which then supplies the glyph. This is called FontLocking here internally and I have made mention of this elsewhere in the forums.
Why we do not fallback to something else properly I am interested in - investigating both failure issues and exposing more control over which fonts are used during fallback is on my list. So this is a useful report to me, thanks for sending it on.