In theory models can/could do the same thing. Think of the current text output of a model being those thoughts inside your head, you have an internal scratch space you work on ideas, then after you perform 'chain of thought' on them, you output to the world. What you're outputting to the world isn't your directly thoughts, but more of a calculation of what you wanted to achieve.
Really for LLMs you just need to have the model put it's output to an internal buffer, read that buffer and make sure it makes sense, then output that to the end user.
It's probably not fast or compute efficient to do that at this time, but at some point it likely will be.