I'm pretty sure I do not have Fontase installed -- I did at one time in the past.
However, fonts in the Users/usename/fontbase/fonts folder are still showing up as available in Illutrator.
When try to delete them, I get an "in use" error. I closed the Adobe CC apps, but it still happens.
NOTE: These font are not visible in the Windows 10 fonts folder...so I cannot delete them there
(I'm trying to remove all the fonts for which I have no license.)
Do the fonts show up in (for example) Microsoft Word?
Yes...they are available in the MS Office suite.
Just to make things clear:
Ok... so this isn't an Adobe issue. Your fonts are installed... they do not need to actually be in the fonts folder to be installed. HOWEVER, the fonts control panel should show all installed fonts. If it doesn't.... you may indeed still have some old font software running and should look into that.