But the thing also is your decks were unable to carry you even without suicide.
I think it's just a matter of allocation. If for the first 4 rounds a team was playing with an extra 30 pillars in its Vault, it should be fine. The key is having enough pillars so that there's no way to burn out. Either general success keeps the supply at a usable level, or general failure burns enough members off of the team that the pillar pool is still sufficient.
In my opinion any team who did
not have an extra 30 pillars,
at least, when they built their first-round decks, did not take enough pillars in their starting Vault.