I dislike this suggestion for many reasons. Just because we're not like every other Survival/Hunger Games server doesn't mean that's a bad thing, in fact, that's what I love about the games, being exclusive compared too the Hundreds of other servers that copied each other, I hope this feature doesn't get added. Many get the Survival Games and the Hunger Games confused. There's multiple Hunger Game servers, and very little Survival Games servers, and most of these Survival Games are all based off these very servers. But besides that...
If the Grace period were too be added to Minecraft Survival Games, it would ruin the anticipation of having too rush to your route with a guy behind you in half iron armor and a Iron sword, that's what makes not having a Grace period fun, if we didn't have that, it would change Player vs Player on the server in a bigger way then just not being able too kill each other at spawn. In the long run, if you really think about it, people will get ten times as much supplies then they normally would without the Grace period. Not only that, I've lately been calculating the amount of deaths at the start of every game, and over around 15 games, 1/4th of the players die within the first five minutes, and that's because there's a challenge on your route, due to PvP being on, now if it was removed during the Grace period, the challenge wouldn't be the same. Also keep in mind, that 1/4th die within the first five minute, now, if you think of it, that lowers the amount of time in each game. Now if the grace period were too be added, that would all change.
The start of the Survival Games is one of my favorite parts, I love the anticipation of any second feeling a blade go through your back, and out your ribs, I believe, that with the grace period, it'll just change the entire games in a negative way.