I'm confused about why you're suggesting the only options are "work together for an entire week" or "don't keep anyone updated about what you're working on for a week".

There are a lot of ways to keep your team updated, but more importantly, it's frankly arrogant to think you can or even should tackle any problem on your own.

Joe is the expert on feature X. When we have a problem in X we ask Joe for help and he invariably provides the insight needed to solve the problem.

When Joe has a problem with X, he should go ask for help, even though he's the one best able to deal with it? Should he ask himself for help?

Can you see the problem with blanket statements like this?

I've been in this situation many times too, but I have to say it feels like a weakness. When a single person works on a problem I see improvements being left on the table compared to when two people effectively collaborate. I've experienced this in a wide range of skill/experience levels so I don't think that is the problem.

That said, I don't know how to change the situation if you have devs with skillsets that don't seem to overlap much, which seems inevitable for some companies

In general I agree, where possible and where it makes sense getting others involved early is a good thing. Somethings are more solo work however, at least for a while to get things oriented. Some times it takes time to gather enough context to even start to express a problem space to others. Not everything is just adding a button to a web page.