7/16" hex bit is used for 9/16-12 UNC and 9/16-18 UNF socket set screws and cap screws. 9/16-12 UNC and 9/16-18 are recognized standard sizes, but they're very rare to find in actual use.
The only two normal applications I can think of are set screws on some Brown & Sharpe taper shank tool holders, and chuck jaw adjusting screws on some older Pratt-Burnerd and South Bend 4-jaw chucks.
If you're not a machinist, you probably won't ever need one, and for that matter, even if you are a machinist you may not ever need one.
But, since a 7/16" hex bit would complete your set, you probably should buy one, because otherwise, that gap in the sizes is going to grate on you, and become more noticeable with each passing year, until finally, you snap under the pressure....
