Further affordability pressure is also caused by the proceeds of corruption and organized crime being used to buy/hold housing as part of money laundering schemes. The sums of criminal money involved in the housing market are non-trivial and have been estimated to account for upwards of 5% of housing valuation in some cities.
Construction costs do not enter into this at all.
If you want to address housing affordability, only three things will make a difference: get rid of NIMBY vetoes on new construction, require all properties that are not owner-occupied to be tenanted, and severely crack down on money laundering through the real estate market.
The US used to have prefab apartment block construction, as did most Western public housing programs, but generally speaking they have not held up over time.
We are also at a cross-roads with regards to having a housing crisis. There are many places now (Bay Area, Boulder) where housing is skyrocketing not because the value is naturally increasing, but is instead being artificially inflated due to a shortage in homes. One "radical" solution to this: build more homes.
However, given the amount of labour and time needed to do so, we may not be able to avoid the housing crisis. One way the market is responding is moving to pre-fab construction, and trying to reduce time / costs that way. The article does seem to claim that the projects cost about the same, even if pre-fab is faster in terms of time. This _does_ identify a problem with pre-fab, namely, how come they can't fulfill this promise of being cheaper & faster. Seems strange that you save time but still cost the same when what you're proposing is taking away a significant chunk of higher-skilled labour from the equation.
Some of this is regulatory capture (wasted time / money trying to convince cities of the process), some of this is nascent technology sucking (see top parent comment, sometimes pre-fab doesn't get it right), and some of this seems to just be a lack of experience on behalf of the companies trying to "disrupt" construction.