Look at foot soldiers. One of the basics of their training is to stop thinking. I don't think that LLMs are doing our thinking for us, though. Not anymore than a calculator did before, at least.
Perhaps so for the most junior grunts, but officers with people under their command are definitely expected to think.
If you are in the military one of the most important things you need to be able to do is perform what someone higher ranked tells you to. Do not think about it, just do it. Doesn't matter whether you are at the bottom or a major. You are not there to question a command, you are there to execute it.
You can think about how to best execute the command and that's it. Without that you don't have a military.
That's not how the US military operates. The Marine Corps, for example, has an explicit concept of the "strategic corporal".