The only thing I know about Time Trials bikes is that they usually look completely insane with a commensurate cost.

I'm looking at a set of brake calipers that are Marketed as "Time Trial/Triathlon" brakes..i'd like to use them on my go-for-a-fast-ride bike
https://www.tektro.com/02products/12qb.php
The example there isn't C&V but this applies to C&V parts just as equally....what makes these parts "TT/Triathlon" ?

my main concern is whether there is a focus on weight savings at the cost of reliability.

It mounts on the backside of the fork to give an aerodynamic advantage.

These days there are only 2 kinds of components that are TT/Tri specific (excluding saddles) : Brakes and levers (which have to fit the ends of bullhorn bars) and shifters (which have to fit the ends of aero bars). Some brakes are designed to work better with these bar end levers. Other than that, components designated as "TT/Tri" (including wheels) are just marketed as that (ok, there is no drafting in TT/Tri, so aero wheels are an advantage, but a regular road racer would get an advantage with aero wheels).