Twinax cables are very high-frequency yet bulky cables that most often serve either of two purposes:
- very early, low-complexity copper connections for new speed grades
- short, low-cost, low-overhead connections
Their reach is usually very low - there's no horizontal or vertical cabling standard for twinax. Structured cabling uses fiber for high performance or high reach.
Twinax has much higher performance (=signal fidelity) than cheap twisted pair cabling - several GHz instead of hundreds of MHz - but it's also more bulky and of much higher cost. Due to the expected low-price nature and better reach of Ethernet, it is only used for early PHYs when a new speed grade is developed or in "niche applications" like short-reach interconnects and stacking.
Twisted pair needs much more complex encoding due to its comparatively inferior frequency performance, so it's only available somewhat later on with a new speed grade - check gigabit or 10 gigabit Ethernet for reference.
The reason why twisted-pair Ethernet came up with the straight-through and crossover variants is that Cat-3 straight cabling already existed when 10BASE-T came up (or StarLAN even earlier) and Ethernet had to find a solution to work with that: nearly all devices use one variant of transmitter and receiver contacts (MDI), except for hubs (and subsequently switches) which use the opposite MDI-X pinout. It doesn't work in all situation, so you'd need crossover cables for connecting like devices.
Twinax (or fiber for that matter) didn't ever have this problem, so there's a signal crossover in every cable, creating an odd number of crossovers in nearly any situation.
Note that the twisted-pair crossover vs straight confusion is mostly a thing of the past as nearly all devices from 1999 on (or so) support Auto MDI-X.