To regard the self (the metaphysical subject) as a container is to objectify the self, which is the very mistake that Wittgenstein is trying to lead us out of. Others have made the same point, as I point out in another thread.
I think this is the “false starting point” (subject as just another object in the world) that Wittgenstein is trying to jolt us out of. It is also the false start that Mait Edey is calling into question in the post linked above.
As you say, “thinking of the subject as container of the world would tend more to generate the solipsistic view,” – i.e. “thinking of the subject as object” (a container) "enables the ‘misguided question of solipsism.’ ”
I interpret the Wittgenstein of the TLP to be telling us that the unexamined impression that we begin with – that the subject is nothing more than an object in the world – is a logical error. Instead, there is a metaphysical subject that is a limit of the world. But it is not a container – the world doesn’t need to be “held together” in that way.
The Wittgenstein of the PI is telling us that he was wrong to think that way in the TLP. He was “bewitched by language,” and he now considers the problem to be that of a grammatical confusion. We mistakenly model the structure of reality on the structure of our subject-predicate form of language, so we unthinkingly concoct the idea of a metaphysical subject and confer upon it a substantial existence.
But you should be wary of taking my interpretation as valid. It is likely contaminated by other views that I’ve encountered along the way.