One question - Isn't it hard switching from thinking about an email for one project and then going straight on to writing another email about a completely different project?
I think this is an individual preference.
I, yep, don't like to switch from project to project when the cost of switching from context to context is relatively small--and for me, if I don't have to get up and go somewhere, the cost of switching from context to context is indeed pretty small. So I'd rather stay inside one project and make a call, use a piece of software, write a bit of a document, etc., all inside that project.
This is true when those tasks involve a certain amount of mental effort, and the context switch involves less mental effort. If I were, instead, printing a bunch of documents, or making copies, or some other fairly low-thought task, then I'd be more likely to remain within a context. If it took a big investment to get into a software tool and get going, I might, again, prefer to switch between projects than switch between tools.
But more often than not, I prefer to stay with a project.
I must admit it makes me feel uncomfortable to think of organising my lists this way (all calls together whichever project they are from, all emails together whichever project they are from etc), as I feel I will get muddled about what I'm working on and miss something but I'm going to give it a try because the way my brain thinks should work definitely doesn't!
There are tools that let you organize your actions both ways, where each action is tied to project AND a context, and you can view them either way.