Saw your post about pre-employment testing. It's been a while since I've had my head in the selection literature, but historically the general pattern of predictive validity for various selection methodologies has tended to follow a consistent pattern. The most predictive procedures tend to be those that emphasize biographical data, primarily work history and education, with coefficients in the .5 range or even better. This is followed by formal testing and is is where it gets a little tricky. Much of the early selection research was conducted or funded by the military, primarily the Navy through the NPRDC (now the NPRST). This is because the military can't spend a lot of time messing around trying to figure out what MOS people are suited for. Therefore, you have the two component tests you describe, an IQ-ish type of test and a group of aptitude-type tests. This kind of testing has relatively high predictive validities, almost as high as those for biographical data. The problem with both of these methodologies is disparate impact. Therefore, employers are going to great lengths to try to avoid correlations with prohibited dimensions. If you want to read something that strikes fear into the heart of HR managers, peruse section 5 of the Uniform Guidelines on Employee Selection Procedures.
The whole federal guideline related to job testing is 16,942 words long. From skimming it, I'd say that, yeah, you could get away with testing. After all, P&G still gives a "Reasoning Test" that looks much like the GMAT that MBA applicants take. But this Guideline is intended to make you think long and hard before trying it. Sure, P&G got their test validated, but then P&G is largely staffed by competent people hired in part through testing. Can your staff successfully jump through every hoop in the 16,942 words?
After all, your managers like interviewing. They each think that -- while everybody else is terrible at interviewing -- they are way above average at it. Interviewing lets them hire people they like. So why risk a federal lawsuit to make them hire people they feel less sympatico with just because they'd be better workers?
What you really have above is one methodology that screens for conscientiousness (work history) and one that screens for intelligence (tests). Privately, Industrial/Organizational Psychology types will tell me that this is really the only thing that matters in selection. The rest is just BS.
The real scandal in employee selection is the almost zero predictive validity of interviews. No matter how they are constructed they tend to contribute almost nothing to employee selection. Probably the best they do is identify obvious jerks, but even that is questionable. The reason we continue to do them is mostly cultural, I suppose. There is also a cult of "personality testing" inside of HR these days, the MBTI seems to be the favored tool, although there are others. This is obviously quite distinct from the AQFT-type testing referenced above.
Understanding the HR field today one has to realize it embodies two very different and often contrary functions; selection and compliance. The first area is dominated by I/O psych types and the second by lawyers. The academic side of HR, in particular university based research into selection, is almost universally populated by the former. On the practitioner side, while most HR people are not lawyers, the legal issues tend to overwhelm everything. This has led to growth in formal structured procedures for all of these types of decisions and associated documentation requirements. Unfortunately, despite all of the attempts to create procedural fairness, the drift has been back into interview type "fit" exercises, and hence what HR people call the "like-me" problem.