As far is I'm aware, there aren't many rational arguments for using the imperial system of measurement in favor of the metric system.
Have there been actual political attempts to establish the metric system in the US? Why not?
All imperial units used in the US today are legally defined in terms of metric units since 1983.
The US officially uses the metric system as the "preferred system of weights and measures" since President Ford signed the Metric Conversion Act in 1975.
Further active 'metrication' of the US was abolished by Reagan in 1982.
As such, there is no need to establish the metric system, it's already established.