Why don’t soldiers usually learn one sign language? Wouldn’t this be useful if you needed to sneak or if gunshots were too loud to be able to hear anything? It seems like the more ways to communicate, the better, right?
The short answer is, they do. Calling military hand signals, “a language,” might be overselling it a little. You can’t carry on a full conversation. However, hand gestures are a very common form of combat communication. Particularly when electronic communications are out.
The primary function isn’t stealth, it’s to be able to communicate in combat, when verbal commands would be drowned out. It is silent, but that’s a useful byproduct.
Because these signals are a combat language, it is preoccupied with being quick at the expense of being flexible. It has numbers 1-10, but after that, the core tends to be focused on orders and warnings.
You can’t express complex concepts beyond giving orders, or relaying tactical information. You can tell someone you see enemies and how many, but you can’t distinguish between a bridge and a statue. The only difference between an order to take and hold either is where you’re pointing. If that kind of information is necessary, soldiers can always switch to their spoken language for more sophisticated orders.
What the signs do is give the commander the ability to quickly and clearly assign tasks in combat, and gives the soldiers the ability to relay information to one another.
Hand signals are not universal; militaries have their own versions. These vary by nationality, to the point that there’s no direct translations in some cases. Additionally, units may sometimes incorporate new, unique, signals to suit their needs, and some widespread unofficial signals may exist.
If you’re wondering why they don’t incorporate ASL (or another sign language), it’s about efficiency. Fairly complex concepts, like an incoming gas attack or a sniper need to be conveyed in a single signal. ASL isn’t designed around that. It is a full language, with its own syntax and grammar. The US Military used to use the ASL signs for 1-9, and used the ASL zero sign as a 10, but that changed at some point, I’m not exactly clear when.
You can’t have full conversations in military signals because, that’s not the point. That’s not valuable for how the system is used. If you need to talk to someone, you talk to them. When the bullets are flying, you don’t really have time for that.
So, the answer to, “why don’t they?” Is, “they already do,” for the reasons you suggested.