Can you quote independent medical research published in a refereed journal to support your claims? If so, please let me know where I can read it (without subscription). Otherwise I am afraid I will have to treat the claim that 'Compression allows the arterial wall to relax, increasing artery diameter' as pure marketing spin. I may of course be wrong, but so far I have read nothing to change my ideas. But, educate me if you wish.
The matter of 'protection from Deep Vein Thrombosis while traveling' is a totally separate issue, unrelated to what is required during activity. In fact, the two situations are directly opposite: when travelling you are sitting down the whole time. The idea here is to compress the leg so blood does not pool in the lower extremeities, and mainly applies to people who have poor circulation. You cannot link DVT to athletic performance. Don't bother to quote 'endorsements' over this: we all know they are simply paid commercials.
We have all seen the claims Nike has put up for the so-called benefits of 'pronation control', 'arch support' and gel soles. None of these have any supporting medical research, and all three of them are consistently rejected by experienced athletics coaches and medicos as being simply FALSE. All three are known to be potentially dangerous for an athlete. We get used to these marketing spins and become very (wisely) cynical.
In addition, I have tried compression stuff myself, and it restricted my blood flow so my legs got cold. Taking the stuff off let my legs warm up. That's experience, not spin. (That might be one way for Jack to test the claim.)
I have an open mind, but you will have to produce scientific proof.
PS - from Wikipedia:
"Compression shorts are also popular among female athletes, especially among those who wear skirts or kilts during games. In those situations, athletes wear compression shorts under the skirt so if they fall over and their skirts ride up, their underwear will not be exposed."