Can you downgrade to socks for the ACFT 2 mile run? Is it considered a no go or is it authorized pending the NCOIC OR OIC organizing ACFT?

NOTE, It appears my info may be out dated, as of late 2021 I do not see a AR or DA PAM 670-1 listed on APD E Pubs

2-44. Soldiers can only wear prescribed APFU components during the ACFT. Any piece of clothing not prescribed as a component of the APFU is not permitted for wear during the ACFT. Neither are devices or equipment that offer any potential for unfair advantage during testing. Soldiers cannot wear the following items: nasal strips, back braces, elastic bandages, kinesiology tape, or limb braces. Biometric measuring devices such as watches, heart rate monitors, step counters, and fitness trackers are permitted. The wearing and carrying of other electronic devices is not permitted. These include electronic music players and cell phones. AR 670-1 specifies the components of the APFU.

So look at AR 670-1 and DA Pam 670-1 for your answer
Chapter 10 Physical Fitness Uniform . 10–2. Composition The physical fitness uniform consists of the following: a. Jacket. b. Pants. c. Trunks. d. T-shirt. e. Undergarments. f. Footwear. g. Socks.

What does the reg say?

I would suspect all the bad reasons to be the guy that tries this, is the increased injury risk just isn't worth it to your chain of command.