I agree with you that language helps formalize and structure thoughts in an intelligible manner, and I do also have reserves on the hypothesis that one can think much faster than it speaks.
Though, is it completely wrong to assume that a neurolink interface would act like a language?
I mean, you mentioned that it would not be possible to probe the whole brain, which makes sense, but I could imagine that to communicate easily with a neurolink interface, you would somehow need to convert your thoughts to _something_ that is probed and intelligible to the interface, just like you do when you articulate sounds to speak.
For instance, if I just vaguely think of moving my hand, that's a pretty blurry and noisy thought. But when I focus, I can almost physically feel that I am at the very edge of moving it, my sensations in the hand increase, my muscles don't move but I feel like they are ready to at any time.
Surely, thoughts that are the result of a specific focus like this could be more easily probed. In fact, it could also be that your brain would need to "learn" how to properly focus thoughts that work with the interface.
That makes for a much less appealing interface though, because it's not "effortless" to articulate thoughts in a specific manner that an interface can probe.