As rare as it might be, there are situations where allies would just leave (Especially on Cradle), but depending on your current commander you can enjoy the rest of the map just fine.
Who is your favorite solo commander when situation arises?
Kerrigan and Zagara are great because they have no top bar, so you’re not missing out on anything there! 
Tychus is nice if I can get Nikira, NOT have her be the 2nd outlaw, while playing as non-Zeratul (otherwise there’s conflict with the ‘W’ keyboard shortcut)
If I’m Karax, any CO that has a basic, AG and AA unit (e.g. Marines, Gollies, Hydras, Goons, Stalkers), which fills that gap in his toolbelt.
Stukov is about as low APM as it gets. His P3 is tops. P1 is worst, but you can still use Barracks to spam Rines even though it’ll set you back a modest amont of mins
It all depends on what map, mission, commander and mutator(s) I end up with. It also depends on what prestige and mastery they have picked. Some examples:
Dead of the Night Brutal 0
Karax P1, Dehaka P1 or P0, Nova P3 are a few I would like since all have good advantages on that map.
Against mutators like Fatal Attraction or any mutator that punishes melee
Dehaka any prestige and Zagara I usually like
Heroes with automatic extractors can also be nice. It depends though.
an expensive commander is best I guess? the extra income will speed you up, you can solo with any commander though, unless we are targetting some specific mutation
Tychus, Nova, Zeratul, heck even Kerrigan.
I recently played a DoN game as HH P0, but my Stukov P3 ally left. Just make as many bunkers as you can, and thanks to another post where somebody said you can squeeze them in like sardines in a can and Troopers will still properly generate, it was easier to get more of them in. Hotkey something that can set Psi Emitter (e.g. Rax, Bunker, or ICC. I used the latter), and the deluge of Infested Troopers will provide a nice suppression system!
If we are talking about a regular Brutal game (No Mutators), then I pick Dehaka. It doesn’t matter the Prestige you chose. It doesn’t matter if you have an ally or not. It doesn’t matter if you use your ally’s resource or not. Dehaka can just win alone.