Isn't space militarization kinda... Bad?..
Nah. If not for Outer Space Treaty, we would have much more advanced space capabilities by now.
Also, arguably the best placement for retaliatory nuclear arsenal is on high Earth orbit. It is constantly under observation from both sides, so neither sudden attack from it, nor sudden attack on it is possible (it would took hours for missiles to went through distance). I.e. no worries about your arsenal being destroyed, and no worries for your opponent that you may launch a sudden attack on it. Win-win scenario.