For most electromechanical industrial stuff, you will rarely need to look at signals with frequencies much beyond 10MHz. At such low frequencies, almost any reasonable piece of wire will be good enough.
I beg to differ and load it with, "it depends."
In characterizing an OXCO product I've been working on, I built up some prototypes of the 10.000MHz output driver. Un-terminated, the following is the 10MHz output on 1m of Tenoslite coax. At 10MHz, the effective electrical length is 20.4m so 1/20th of a wavelength shouldn't matter... right?

This is pretty ugly, and the chatter right in the crossover zone may lead to glitching. This is the result with not even "any old wire" but relatively good quality coax. Let's see what happens when that same output is put to the scope directly, with essentially a BNC barrel stub into the scope, still unterminated:
Similar issues, and while the waveform is "usable" it has no capacity for transmission length. How about the primary use-case when it's properly terminated, and using the 1m of Tensolite?

Perfect.
What's the catch? "10MHz" is relative. If it's a sine-wave, then a stray piece of wire
may be sufficient. Start moving to square waves, and you get very rich harmonic content depending on your driver's capabilities. In this application, I needed razor sharp edges and minimal jitter as primary requirements. A wish-list item was to have something that was viable for standard logic level operation in an unterminated condition. Once you're talking about square waves, especially ones with very fast edges, you have a
lot more than just 10MHz, but 30, 50, 70, 90, 110... etc. With some degradation, you can pick a coax which has minimal losses for at least 5x your fundamental.
OP mentioned "400MHz" which is actually kind of meaningless. These things don't just "brick-wall" stop operating, but rather have a spec on losses vs. frequency. It is these losses which screw with the signal seen on the other end of the coax.