Generally in these situations, I'll switch to a healer or tank (depending on team comp & performance).
No healer? Lucio, Mercy, Roadhog, Zenyatta.
Bad healer? Roadhog, Lucio, Zenyatta.
OK Healer? Any tank.
Most of the people aren't as terrible as we think... It's just they don't play objectively, or try to rush in solo. Switching to a healer (even if you already had one) can sometimes delay their deaths long enough for your whole group to actually group up, or very rarely they'll congregate around you so they can keep getting HP. If just a healer isn't going to do it, or you already have an acceptable healer, then switch to a tank. Zarya is a good call if your healer heals... But doesn't stay alive. Roadhog is great since it'll let your healer focus on everyone else while you self heal. Reinhardt, D.Va, and Winston are more team reliant unless you're flanking (in which case you probably will still lose with a bad team that isn't playing the objective), so go with one of those selectively. I'd only go Zenyatta over Mercy/Lucio if your team is having trouble with a Bastion or your DPS just suck (which, if Bastion is the problem, is likely the case) and you need to keep dealing damage while being able to heal. Roadhog is my go-to in these situations simply because of his skillset and being 100% self reliant, tho that might just be a personal preference.
Another option is Lucio or Genji (depending on how your healers/dps are doing) for when you just need someone to get on the f*cking point. They're both highly mobile and I've stayed on the payload after the other 5 members of my team were eliminated long enough for them to come back and still survived by just jumping around and using the payload/environment to block LoS. Which is the better choice matters a lot on the map too, Lucio can dodge better in tight spaces where Genji can do his evasive dance in the open and still survive if done right.
In all reality tho, carrying a team solo probably isn't going to happen. The best thing you can do is to assess the situation, figure out what's wrong, and do your best to fix THAT solo.