Can’t speak to the skill question, but as for whether they should have grenades, depends on their status when the thing went down. We’ve got the recruit, the activated national guard, and the pilot for normal soldiers afaik (I play with a lot of mods, so I might be missing some). Additionally, there’s the special operator, and then the bionic soldiers.
I’d be hard pressed to believe that they’d give an untrained recruit grenades to go out and deal with what was thought to be a riot scenario. The fact you got a gun and got deployed at all is surprising, so this could go either way, depending on whether you assume the military practically threw the armories open.
The national guardsman’s kit indicates he was off-base and was activated. They won’t let you off base with a rifle, much less with hand grenades, so I wouldn’t expect to start with them.
As for pilots, I can’t see why a pilot would be wearing grenades, but at least he’s in theory actively deployed, so its the most plausible of the bunch. Smoke grenades would make more sense as signalling devices.
For the operator, and the bionic soldier, I could see grenades being part of the kit, both lethal and non-lethal. I’m not sure these classes need any more lethality, but they’re already crazy so whats a bit of consumable ordinance.