I think its a deeply complicated set of problems - and open sourcing wouldn't be a magic wand for a lot of it.
I suspect quite a lot of the 'backlog' is things that might be fixed or obsolete, but no one really kept track or things that are wontfix/not really a important thing as far as the company is concerned. I don't think the raw numbers tell the whole story outside, there's a lot of tech debt over time, and there's not enough caffeine to go through all of it.
Charcoal exists cause existing official tools weren't good enough, and the loose coupling helped a bit. Its a small team, focused on a specific problem with broad impact on the network. To me, it feels like an anomaly. Contrast that, with say replacement mobile apps - which are mostly possible but don't exist.
I'd say there's a handful of issues, that are mirrored both on the company, and community side - that resources aren’t always community focused (and if parts of the code are open sourced, we'd still need company support to review and merge code contributions, and figure out an appropriate licence for these contributions.
That also means that potentially a good community contribution might not work out either cause its one person's passion project, or cause its just not something the company wants to touch on right now.
I'd note there's small parts of SO that're open sourced now and a very quick look suggests most PRs are either by former or current staff, and compared to MSE, the issues are sparse.
Critically, the company's likely to still be calling the shots on what's worked on, so it would be essentially extracting work from the community towards the company's goals as much as ours.
As much as open source could be a solution, we'd likely get a lot more headway from appropriate resourcing, and better alignment between the community's needs/desires and what the company works on.
score:3.. is:q closed:noto the searches cuts both of them down by more than half.