Well, I think that this vid amply demonstrates why this design of grenade has not been popular since WWI. It is just a more simple (ie cheaper) safety feature than the conventional grenade's safety lever, but the drawbacks of a sticky pin can be considerable, although this is almost certainly a very extreme case.
Out in the field, there is nothing stopping someone pulling the cord and then throwing it like a conventional grenade, but given how short the fuse was in that video, that is probably not a great idea.
They may have made the fuse so short to dissuade soldiers from the temptation of 'cooking' the grenades, but since the greatest design advantage of a stick grenade over a conventional one is that it is easier to achieve greater distance with a throw with a stick grenade, I believe that the choice to set the fuse so short and the practice of relying on momentum to arm the grenade is intended to maximise the possibility of an airburst over an enemy position.
To prevent a sticky pin from causing the grenade to drop dangerously close, you are best off lobbing the thing as hard as you can. With proper technique and a little experience, it would not be all that hard to be able to achieve air busts fairly consistently. That would hugely amplify the lethality of the grenade as well as it's effective range.
In tight spots, where accuracy and finess are key, you can always pull the cord out before throwing and be able to get just as much control over it as any conventional grenade.