This sounds very suspiciously of a problem that existed in El Capitan. There was a problem related to files in a deeply buried system framework that was causing the issue. Because of it, these five fonts did not work correctly.
Athelas.ttc
Charter.ttc
Marion.ttc
Seravek.ttc
SuperClarendon.ttc
Just as you're seeing, third party apps would see and use them, but not Apple supplied apps such as TextEdit.
I thought this had been fixed in Sierra as of the beta 3 release and later. I haven't been able to recreate the problem in the official release of Sierra.
No, you shouldn't be able to see San Francisco fonts in any app. While the entire set are standard OpenType PostScript fonts, the internal names define them as system fonts and are blocked from being used beyond the interface.
Just to check, see if the one of the fixes for El Capitan solves the issue. An excerpt from my article that explains it:
As installed by OS X, these fonts don't appear in TextEdit at all, only partially in Mail, and so on in the Apple supplied apps. At the same time, they would function normally in the Adobe CC apps, Office 2016, Quark XPress 2015 and other third party apps.
If you simply rename the fonts on the desktop, they suddenly work in all apps! Okay, why is that? The file name of a font quite literally means nothing as to whether it will activate or not. So why did it work for these? The answer has to do files installed deep in the System folder. The OS installs font name matched .ATSD and .fontinfo files in the /System/Library/Frameworks/ApplicationServices.framework/Versions/A/Frameworks/ ATS.framework/Versions/A/Resources/FontInfo folder for every font OS X installs. Such as this for Marion.ttc:
Marion.ttc.DF798_0.ATSD
Marion.ttc.DF798_0.fontinfo
They've been there as part of the Mac OS for a long time, but until now, never really had any logical reason to exist. At least not to me. Since this issue didn’t exist before El Capitan, they now appear to be tied to System Integrity Protection. We believe this is what’s happening.
1) The .ATSD and .fontinfo files haven’t been correctly updated by Apple for these five fonts. As such, it considers those fonts as having been altered. Being altered, SIP assumes possible malware injection and refuses to use them.
2) When you rename those fonts, SIP no longer has a file name that matches the protection scheme and considers them third party fonts.
3) The only part of this that is still somewhat off base is that these five fonts still don't work even if you have SIP disabled, and renaming them still fixes the problem.
4) When you replace these first four fonts with the Yosemite versions, then the expected data must match the .ATSD and .fontinfo files, as they then work without renaming the fonts. Super Clarendon remains unrepentant no matter what version of OS X you copy it from.
You can prove the issue is tied to these framework files by moving the .ATSD and .fontinfo files for those five fonts to a new folder on the drive. Now enable the normally named El Capitan fonts in any font manager. With no reference to them in the framework file, the OS considers them third party fonts (or something) and they work.
There are three ways to get around this. The first two require first temporarily disabling System Integrity Protection (see just below how to do this).
1) Rename the fonts. Like Marion.ttc to MarionE.ttc. It literally doesn't matter what you change the file name to.
2) Leave the file names as they are and remove their matching .ATSD and .fontinfo files from the framework folder.
3) A few more steps, but this still takes less time than disabling SIP to perform 1 or 2, and then re-enabling SIP.
1. Highlight each of the five fonts and press Command+D to duplicate them. For example, this will produce an "Athelas copy.ttc" file.
2. Highlight each original font and choose Get Info from the menu bar, or press Command+I. Change the permissions of each to add yourself (the admin account user) with Read/Write privileges.
3. Move the original, normally named fonts to the trash and restart. Empty the trash.
These same fonts also didn't work in the Sierra beta until just recently. The beta 3 update has fixed the issue, so you can expect the fix to carry through to the final release. Whether or not we'll see another point update for El Capitan to fix it in this version of OS X remains to be seen. But at least you have these three methods to use if not.