Bar width makes little difference in reach. It is more a matter of breath (too narrow is bad), wind resistance (the narrower the better) and handling (bike will feel more secure with wider bars, turning is a little slower).

On the first point - breath - the old "rule was that you didn't want to go narrower than your shoulders. We would pick up bars we were thinking about and placed the bar ends against the balls of our shoulders. An exact fit was considered good (and served me very well racing).

I put very wide HBs on my "mountain" fix gears for better leverage climbing. Nice side benefit - great control going very fast at high RPM downhill. Second benefit - less aero going very fast downhill at high RPM. (Less aero is better you ask? When more aero means spinning even more ridiculously fast, yes, you bet!)

There is also riding in the peloton if you race. Wider - better for the bumps with other riders that happen. Narrower - you can fit through smaller gaps.

So you can see handlebar width is a compromise.

Ben