The point of the match isn't to have tension that it could end at any second.
The point of the match is that whoever has the advantage is supposed to beat the shit out of the other team, because the match literally cannot end before everyone is in there. That's why the best War Games matches are bloody, violent, and aren't WRESTLING matches.
You not being able to lose by pinfall means your options are either getting the shit kicked out of you so hard that you pass out, or you face the shame of submitting and being the reason your team lost.
Being able to be pinned means that it misses the whole point of the match.
No talent should want to be in a War Games match unless it's the only thing that can settle a feud. It should be like a Hell in a Cell, where you only break it out when it absolutely is the last resort.
