My understanding is that installing strapping originated from the need to create a flat surface for attaching a ceiling to the uneven hand-hewn timbers once used as structural framing members. Carpenters shimmed the strapping down to the lowest point in the room and then attached the finish material. While we no longer need to shim the strapping to achieve a relatively flat ceiling, the board hangers that follow behind us appreciate a full 2 1/2 inches to attach the board to rather than the 1 1/2 inches provided by dimensional lumber.
The trades that work in this area always appreciate strapping. Electricians can use the 3/4-inch space to make long runs perpendicular to the floor joists without having to drill holes.
Strapping in existing ceilings also makes snaking wires much easier. Plumbers can also save labor by running their 1/2-inch PEX tubing below the joists; and they can use the strapping to support waste and vent pipes at the required pitch.
Strapping makes it easier for us to install interior partitions, too.
We strap the ceilings after all ceiling and bearing-wall framing is finished. Working in teams of two, each carpenter begins by laying out an end of the room at 16 inches on-center. When the entire room is laid out, we snap chalk lines on the ceiling to ensure a straight and clean installation.
After snapping all of our lines, we lean lengths of strapping against the top plate at one end of the room. One carpenter then picks up a piece, places it on the line, and tacks it to a joist roughly in the middle of the length of strapping.
He moves across the room tacking all the strips in place, then nails the starting end of each piece.
At the same time, his workmate saws the pieces to length in place, staggering the lengths between joists. For us, this method is faster than measuring and pre-cutting the pieces. After the cut ends are nailed up, the carpenters move across the room adding full lengths of strapping. Once all of the full-length pieces are tacked in place, one carpenter cuts finish pieces to length ...
... while his partner nails off the entire room, with the nail gun.