... originally, a TAPAS type test (under a different name) was used for pilots.
The test you are referring to is the ARMA—Adaptability Rating for Military Aviation.
AFI 48-123, MEDICAL EXAMINATIONS AND STANDARDS,5 NOVEMBER 2013:
1.5. Adaptability Rating. Adaptability Rating for Military Aviation (ARMA) and other military duties, such as for Marine Diving Duty (MDD), Ground Based Controller (GBC), RPA or Missile Operations Duty (MOD) etc., is the responsibility of the examining flight surgeon, as is the scope and extent of the interview. Initial (entry into training) unsatisfactory adaptability ratings are usually rendered for poor motivation for aerial or SOD adaptability, or evidence of a potential safety of flight risk, etc. (see Medical Standards Directory and Physical Examination Techniques.
Origins of military-screening and-selection procedures being developed trace back to WWI with most of the significant initial research and developing happening during WWII.
The problem of gaming the test (cheating or faking answers) is certainly a weakness of such tests. The utilization of computerized testing that limits ability to go back and change answers some what complicates opportunity to faking a pattern of answers.
The limiting the test to one time is actually connected to having numerous variation of test battery available as much taking test second time to game the test to get the desired result.
Regarding "administration of the TAPAS was easier for brand new recruits entering MEPS", the easier applicant/candidate demographics is individuals having no prior military service (meaning has not gone through BMT (Boot camp). Going through Basic Military Training involves personality and emotional adapting to military activities. The adapting that occurs during the successfully getting through BMT skews the testing to needing a higher quality or level of discernment. This adapting that occurs once exposed to certain types of military training is also why TAPAS has not been implemented or likely to be implemented for screening and selecting officers to be CROs and STOs.
Considerable consideration to implement TAPAS or rather personality assessment testing to screen and select enlisted pararescue candidate/applicant emerged in 1993. Connected with this effort was serious political influence that such testing would, could, and will replace the need for the Pararescue Indoctrination Course. This political influence was spearheaded by seriously misguided officers and fortunately they didn't prevail in their efforts. However, the TAPAS development effort continued with Pararescue students being the majority of the research studied participants from 1993 to 2012. The other AFSC were tagged on years later and I'm not sure how much these other AFSCs were researched.
The folks at AETC/AFPC have not gotten back to me so my following paragraph comment is speculation.
The mandate is to open all currently closed to women AFSC to women by 2016 complicates TAPAS as there is currently no female TAPAS personality profiles to use for these AFSCs. Regardless common sense indicates TAPAS not be used for females seeking the GTEP enlistment contract for PJ, CCT, SOW, and TACP. Both SERE and AF EOD have been open to women for decades, so not an issue for those AFSCs.
BTW, the effectiveness of ARMA has always been controversial for many reasons. However the only military pilots undergoing any significant psychological or personality screening (mostly during the 1950s and 1960s) were those screened and selected to be high altitude reconnaissance pilots (U-2/SR-71) and astronauts. As most of these pilots were detailed to other agencies (CIA/NASA) it wasn't the Air Force, Navy or Army actually doing the screening and selecting.
The The operational heritage of the Pararesc...nt demographics
document gives a good historical overview of origins of screen and selecting studies conducted during and immediately after WWII. It then proceeds to give an overview of formal enlisted screening and selection courses being developed and established in the Air Force.