They are included with your Creative Cloud subscription and available for you to use as long as your subscription is active. That said, you are welcome to whatever fonts you like in InDesign. You don't have to use Adobe fonts.
I understand this. What frustrates me is that Adobe sometimes discontinues fonts. So, if we use a font for something that needs to be reprinted, but they discontinue it, we're just out of luck--especially if the font is built into an indentity program.
All font foundries are moving to a "subscription model" for delivering fonts. The consequenses to designers are:
Some foundries are very creepy about these controls, but Adobe is (at this time) fairly lenient. They are free (at this time), can be embedded into digital files (at this time), and Adobe doesn't charge extra to use them in one type of file versus another (at this time).
Most likely, your font was removed from your system because the license between the font designer and Adobe expired.
Suggestion: when designing branding items (logos, etc.) that you want to keep around for a while, don't use a subscription font and instead purchase a "desktop" font (a traditional font file you download and install into your operating system). Check the EULA (end user license agreement) so that you have the rights to: embed the font into a file (such as into an AI, EPS, PNG, PDF, etc.); you can convert it to outlines/paths and alter the shapes of the letters; and you can keep the font file for an indefinite period of time.
And keep a copy of your purchased font files somewhere safe off your computer, such as on a CD, file server, external storage device, cloud (but not an Adobe cloud), or flash drive. Everytime we launch a program, software companies are constantly "looking" around our computers for their software and whether you've paid your bill. Keep your purchases safe!
A recent blog talks about these font issues at https://www.pubcom.com/blog/2019_12-06/font-licenses.shtml
Thank you, Bevi. This is helpful--and a bit alarming.