I have worked on both types. I helped build several halls the "slow build" way. This was grueling. You get off work then you go help build the KH. Saturdays, Sundays are taken up helping to build the KH. Budgets were also blown. It is difficult to plan what costs will be for a construction project that will take one to two years to complete.
I was very involved in the quick build program. I led two of the crews, carpentry and interior finish. (I am a master carpenter and a I was a big fan of the quick build approach because it took such a huge burden off the local brothers. I have been one of those local brothers shouldering that burden so I can speak from that point of view.
Every quick build I worked on was run in the most professional manner imagineable. All the key trades were led by master tradesmen. We had licensed engineers on site to do inspections. I don't know if all the quick build committees did it that way.
I don't agree that doing something fast means doing it poorly.
As far as safety goes every quick build I was involved in far exceeded the local building codes. I would say that these buildings were safe.
As for a fire being caused by a faulty electrical box, I guess such things have happened, in all the years I was involved in the quick build program I never heard of a case of any kind where bad workmanship led to a serious problem.