Why is blocking never placed "sideways"?
Horizontal blocking IS used with 2x lumber on edge for non-structural reasons: grab bar blocking, plumbing fixtures (notably freestanding wall sinks) and kitchen cabinets.

Its usually shifted to the front of the wall, just behind the drywall.  For sinks, 2x6 is usually used, allowing a range of mounting heights, ditto for grab bars in baths and showers.

One time for a steel stud wall in a basement, I used an entire sheet of 3/4 plywood over the studs and under the drywall.  It let me freely mount upper and lower cabinets for a bar area.  

In the case of a 2x6 "wet wall" (used for plumbing, especially drains), the blocking can be "let in" in a continuous piece for additional strength, spanning several stud bays.