TOPIC:

I tried a binaural recording of some audiophile class sound reproduction. I was hoping the quality of the recording would be "close" to the source, but it's not. Not at all good quality. What is expected in this type of use? Is it possible to upgrade the mics in the ears if it turns out that the recording quality just isn't there?

EARS is not designed to be an audiophile grade binaural stereo microphone.
It was never meant to be a budget $199 alternative version of a Neumann KU100 binaural mic which costs $6000+ or similar.
If that's what you want, just buy the Neumann if you can afford it, or have a look for some cheaper binaural mic alternatives such as 3Dio, which are designed first and foremost for making binaural audio recordings, and will likely sound better at that task.

EARS is not a dummy head microphone, because as you can see, there is no life size dummy head occupying the volume of space inbetween the earpads, and it will not therefore recreate the vital HTRF (Head Related Transfer Functions) associated with dummy head binaural mics. You might be able to make yourself a DIY dummy mannequin head though and experiment with that? Some people on YouTube have done. Also EARS built-in pressure gradient omni condenser mics are not necessarily equalized for listening playback to sound like free-field stereo (as some binaural recordings are in post-production) and so straight out-of-the-box, the EARS mic capsules raw output - without any COMPENSATION curve correction - will probably not sound like a professional binaural recording.

Yes, admittedly, it is a happy coincidence that EARS is also able to function as a stereo /binaural microphone, if you just record its live output, but that's more of secondary extra benefit than the main purpose of the product. It's interesting to experiment with and adds some extra appeal to buying it, but that's not what it's really for.
Likewise you could use a Neumann KU100 binaural dummy head microphone as a headphone measurement test rig. It would probably work for that function as well.

But first and foremost...
MiniDSP EARS rig gives you a practical way of taking COMPARITIVE pressure amplitude measurements between different sets of headphones under very similar controlled conditions, so you get results on a level playing field, and can make meaningful comparisons - which is otherwise a difficult task to reliably measure headphone's output due to their awkward shape and their need to remain tightly sealed acoustically against the ear surround, etc. Can't just put a handheld mic grille up next to the headphone, it doesn't work like that.
EARS is about the most affordable consumer solution to reliably take serious headphone measurements, and an excellent product for that.

The main technical performance demands for EARS is simply to acquire freq response measurements from headphone drivers placed on the rig.
The condenser mic capsules inside EARS don't require particularly super low noise spec or inherent absolute flat linearity to perform this task - obviously they aren't because they come with a calibrated compensation chart for correct measurement linearity, and are typically just measuring the loudest peak magnitude of a sinewave sweep where the S/N ratio will be pretty good anyway, not trying to record ultra fine low-level details buried in the noise floor - those doesn't matter much in this sweep test type application.
As long as EARS can help you graph the overall frequency vs amplitude vs phase response measurement, it has done its intended job, and after the calibrated compensation curve is applied to correct the inherent linearity deviations, you've got a reliable measurement of your headphones which can be compared with others in a consistent similar method. Do these Beyers sound more midrangey than these Sennheisers? Yes, so measure them both on EARS to find out how much difference exactly and what EQ settings you might need to make them matched.