It doesn't have to be a federal law. Change can start gradually with private companies. Pokemon Go, for instance, shows only kilometers and doesn't offer imperial units as an option. All water bottles in the US have both mililiters and fluid ounces on their label.
For instance, a 4 x 8 foot sheet of plywood down at Home Depot isn't really 4 x 8 feet; it actually has an imperial measurement of 47.938 x 95.938 inches, which is approximately 1217 x 2437 mm - the standard metric size is 1220 x 2440 mm:
http://cwc.ca/wood-products/panel-products/plywood/sizes/
Thicknesses (as noted in the table too) have similar "whole" metric numbers. You see this also on some (not all) general materials sold to the American consumer public - the actual material is metric sized, but marketed with imperial measurements.
I think this is done both for cultural reasons, as well as just "momentum" and that the public is used to it. But the reality is (almost) everything is now metric, the public just isn't fully aware of it yet.
Also, since the gap between plywood takes space, plywood (and drywall) is a bit less than stated size to give you breathing room to put 4x8s repeating every 4 and 8 feet.
That said I don’t know why a nominal 2×4 is actually 1½ × 3½. Used to be finishing work shaved it down, now they just make ‘em that way to be ornery.
That's actually required by federal law. A lot of commercial regulations in the US require metric measurements in addition to imperial.
Don't tell people who are annoyed by metric, but all the 'imperial' units we use now are 100% based on metric units. Our metrology has been metric since that time, all the day-to-day usage is derived units.
Which is why an inch is exactly 2.54cm instead of some rounded fraction.