A punch bow costs 25 diamonds, which is not that easy to get
The bow with punch is somewhat expensive, 25 diamonds,
I see people saying the punch bow is expensive. Well, let me prove you wrong. Let's get an example of solo Eggwars:
You are in the map Mine. You rush the minecart which has 5 diamonds on it. You run back to your island to get blocks, break your neighbours egg and kill him. After that you get back to the minecart to get 5 diamonds again. But now you are going to the middle to get the 10 diamonds. Now you have 20 diamonds in what time? 3 minutes of gameplay (If you're fast enough)? You are going back to the minecart on your side or if you are brave and tryhard enough you can go to one of the other 3 minecarts to take out another player. You take the 5 diamonds again from the minecart on your side or from one of the others. Now you have 25 diamonds in less than 4 minutes. Now you will say "But then there are only 2 guys alive." -Wrong. In solo eggwars people love to camp and maybe half of the game is still alive. Maybe not all with an egg but they are still alive. So the 4 minutes you've spent to obtain 25 diamonds wasn't really a waste of time.
It's the same for Team Eggwars. If you are fast enough with your team, you can get the diamonds from the side islands and from mid. Then you have 25 diamonds in less than 3 minutes for sure (I don't really play Team Eggwars that often, don't blame me for that).
Conclusion: The punch bow can be used as a strategy when you are low. Just bowspam him and maybe they will fall into the void. Or if you are the type of guy that loves long games, you can dominate 1 minecart and middle to farm 64 diamonds to buy an enderpearl, pearl behind him and shoot him off with your punch bow. After that you can break their egg.