Not military myself, but my son is Army, so I can only speak to his experience which he has shared with me. In Basic, he wasn’t allowed to carry anything that wasn’t issued to him and only when they said so, moreover, there was no need to. Even during AIT, his pocket knife (a Benchmade Griptilian) got scrutinized a couple times. After Basic and AIT, he had a lot more leeway. After he got settled in his duty station, I gave him the choice of several knives for field exercises and/or deployment (because dear old dad is still good for something). Of them, he chose a Becker BK10 as being the most practical for the things he’d likely need a field knife to do. It’s definitely not a HSLD combat knife, but he tells me all the time how useful it is.
Another thing to remember is that, although we would hope there’s honor among all service members, it is well known nice things have a way of, shall we say, wandering off. It may not be wise to carry expensive, self-financed gear until your footing is sure, especially on a starting pay grade.