The F connector was designed as a cheap and dirty alternative to other connectors of the time. It was easy to install and aimed at less critical applications like TV antenna and cable TV. While all connectors have a characteristic impedance the slight mismatch can often be overlooked with most applications today. It is the cable itself that will cause the problems.
I stand corrected. I guess L-com makes a F connector for RG-58. Why would anyone want to do that?
The first thing that comes to mind is the ease of installation. When used with an F to BNC (or other like UHF) adapter all should be fine. RG-58 was widely used in the days before ethernet to wire networks. With those T connectors I can't believe the impedance of the cable connector matters much. Many techs shy away from the BNC because of the need for special tools and difficulty of installation.
But my question again is what is the application? If someone got a deal on RG-58 and they are using it to wire a house for cable...
-Hal