I'm not so sure. If you're shot or suffer other injury that affects mobility, it's really helpful to have some comrades around with enough upper-body strength to carry you somewhere where you can get help, or at least cover while waiting for it. Being able to carry a lot of equipment is also useful.
So let's think about what's needed for soldiers to engage in hand-to-hand combat:
1. They somehow need to lose their main weapon.
2. Their sidearm.
3. Be on the front line.
4. Somehow find an enemy soldier that also lost their main weapon and the sidearm.
5. Engage in hand-to-hand combat.