I'll agree with Takai (funny name, wasn't it taken from Harry Harryson SGF novels about Steel Rat's adventures?): the grenade's throwing must be two-stepped: prime step and the throw itself.
In real world the soldier holding a primed grenade may be killed, wounded or just can stumble upon something, and his movement may cause the explosion "in-place" and the soldier's environment, i.e. his team members, may be destroyed/damaged.
Well, I see no need in "priming timer" - standard grenade (at least Russian RGD-5 hand grenade) trigger gives us about 5 seconds before the blast. And the grenade may even explode during its flight, if thrown properly. (very risky usage. I have some training on that, but I'll never try to do that - I'll not to lose my fingers or something more vital)
Priming of launcher's grenades is absolutely useless.