Actually a good question, and I am not sure why Adobe does this. When I have had to fix a machine withfont problems in one application and not the other, this was the reason.
If there is a font you woudl like for another application to use, I woudl make a copy on your drive to your own font liabrary and use font book or your font manager to load this for all applications to use.
At one point I removed all the foreign language fonts (cause I have no use for Korean, Japanese, Chinese and wanted to shorten my font menus), and my system started up with all the files on the desktop having no name (Whcih made no sense, since my system was not using Asian fonts to display that). So I would recomend leaving a copy in the exisiting folder of fonts that applicatiosn insitall, unless you really have the time to troubleshoot and are tech savvy enough to get yourself out of a mess.