These are the traits I've learned that form the basis for a good anthology campaign:
A complex setting which demands a humanistic approach
A system that is adaptable enough to handle many different types of situation - not so specialized that you can't switch from games focused on art, to combat, etc. etc. Generic systems are a good starting point here.
Games that don't rely on teamwork, groups of characters, or PVP interactions to fuel the mechanical conflicts of the game.
Settings that are broad enough to encompass many approaches: the military story, the adventure story, the romantic story, the crime story, the political story. Wars and fighting are only suitable in this way if you can also come and tell about other things that the wars affect or are affected by.
In the tabletop RPG space there are a lot of candidates that fit these criteria. Here are some that I've thought of which I might try anthology campaigns for in the future:
World of Darkness. I'm quite excited to look to both the classic "dark carnival" World of Darkness and the 21st century "modern horror" World of Darkness games to see how they might change with a relentlessly individualistic set of adventures.
Traveller. The libertarian dystopia of debt, war, warlords and criminals lends itself very well to the kind of highly focused noir that a one-on-one game can provide.
Star Trek. Not until Discovery and Picard (arguably) did Trek focus its space opera adventure on a singular character instead of a communal experience. Could we do better?
Highly detailed fantasy worlds in general might be a good idea (Forgotten Realms, Ravenloft in the "independent setting" mode), though some, like Middle Earth, have at their core a story of partnerships across cultural lines which might make a single-player story hard to swallow.
Historical one on one games allow for the tracking of "exceptional" individuals in a way that doesn't betray a historical aesthetic in the way that a "group" of exceptional individuals sometimes feels it does. Essentially the whole of historical romantic fiction is about one person thrust into the key parts of a dramatic historical moment. This could be a good way to get a sense of that moment one-on-one! In GURPS (one of my more favorite historical games) you might truly feel the pressures of that un-obtainably big skill list if you didn't have a team of fellow PCs to fall back on in an unfamiliar situation.
Cyberpunk has always had a core of noir in it - the individual trapped in a skein of their own making. And alone, in a one-on-one game, the ability to fall back on a team might be difficult. Take Interface Zero or Cyberpunk 2020 or even Shadowrun (though I don't necessarily think the Shadowrun system will produce much of interest here.)
A singular superhero game might be interesting with an emphasis on life outside superheroing - take Spiderman, where he's one guy, having to deal with work, schooling, romance, friends, and family as well as whatever bank the Rhino is robbing this week.
Some games that wouldn't work:
Most of the Powered by the Apocalypse games either rely on some degree of PVP (Apocalypse World, Urban Shadows) or teams (Zombie World, Masks) in order to really run. For example, Cartel worked well in this anthology because I had four people playing! I think there's other systems that are stronger for duet structures.
Dungeons & Dragons - the core activity of D&D is too limited and the system is too connected to that core activity. Besides, I don't want to in any way contribute to the absolute scouring of the hobby D&D is undertaking at the moment.