Having done work recently comparing Scope (Tek) and VNA (Agilent + R&S), it was very clear that VNA (probably because of the greater bandwidth of a digital pulse vs the VNA source / narrow band detector) just do not resolve faults that the scope can see.
Cost, size and user-unfriendly user interfaces of all the big iron boxes above does limit the usability in volume production, but there are now more affordable sampling scopes (eg. PicoScope 9xxx) that cost one-tenth of the price and are the size of a paperback book (if you remember them?).
PS: I'm not affiliated to any of the above companies, just a user trying to find an effective TDR capability.
A company called LiveWire Innovation has a TDR technology called SpreadSpectrum TDR which works over any live energized circuit and gives accurate impedance information no matter the voltage, current or noise on the line. It not only detects impedance mismatches but locates and characterizes them while the line is powered. Opens, Shorts and intermittent Arc Faults on energized cables.