Alfred Hitchcock's "Rear Window" -- can you help me understand something about the plot?

I just finished watching “Rear Window” for about the 100th time in my life and noticed something for the very first time. Jeff, the wheelchair-bound voyeur played by Jimmy Stewart, is a professional photographer, and throughout the movie he uses a camera with a telescopic lens to watch a man in his apartment across the courtyard whom he believes murdered his wife. Yet… he never takes photos of the man’s suspicious actions, many of which, it seems to me, would convince Jeff’s skeptical detective friend much sooner that a murder had indeed been committed.

Okay, I know this is the script’s plot device to keep the movie suspenseful to the end, but is that the only reason Jeff never takes even one photo? Would such furtive evidence collection have been unlawful?