I heard a costly system from Esoteric.

It's always troubling to me to hear about the 'faults' like the ones you described coming from uber expensive gear. When paying that kind of money, you expect near perfection. I considered the F-07 at one point but decided on the Luxman 505uxii integrated. I have the Sennheiser HD-650s and they sound great with the Luxman. Just from what I've read here on Audiogon, Luxman seems to have a much better reputation that Esoteric. Isn't Esoteric owned by Technics? 

  I have no particular agenda about Esoteric, but your statement at the beginning, about judging an integrated amp by the way it drives headphones, is frankly a head scratcher.  As mentioned above many manufacturers supply a headphone jack without tuning their equipment for the special needs of headphones.  In general you will do much better with a dedicated headphone amp, especially with the much more demanding headphones that have come out the last decade or so.  

Agree with mahler123 ^. The crummy little chip driving the phones should have zero to do with the actual driving of the speakers...

Thank you for your impressions about that Luxman amp driving the HD-650s. They’re great headphones! Esoteric is the higher-end of TEAC. The CD player track-seeking function, like I said, was a huge disappointment. This is a component that can be hooked up to a "master clock" with near-atomic levels of accuracy. Perhaps it needs that clock attached to it to have faster seek times? I don’t know, but still, for 13k you can do a lot better I’m sure.

To all, regarding the headphone out and the sound quality from it.

If Accuphase, a company who is apparently at the same caliber as Esoteric and has an optimized headphone out on their integrated amps, then why can’t the F-05 have it too?

Why include a useful feature on an audio component as an afterthought? Especially at this price...it just seems illogical. For instance, let us assume that one or more of their customers [Esoteric] wanted to use the amp for headphone listening after work, and speaker listening late at night?

Esoteric product descriptions and marketing material in general likes to use a lot of flowery language: lavish, luxurious, and 36 bits of dynamic range processing on their D/A convertors. And the K-03 appartenly has 4 DAC chips for each channel (L/R) so 8 in total! is all that really necessary to achieve great sound quality?

The other thing I don’t get is the weight of their CD players and amplifiers. I mean, for an integrated amp, or even a CD player, does it really need to weigh 70 pounds or more?

If we have it on an audio stand, a shatterproof, tempered glass desk, a workbench with a cold-rolled steel surface/heavy duty wood, or any other ideal place for audio components, how does such heavy casework on its own improve sound quality? Just seems excessive to me.

Strangely, the F-05 literature mentions "dual mono at every stage" but it only has one 1 EI power transformer. I guess they simply wired it differently. Another strange thing. in some songs I’m very familiar with, when the stereo image (vocals or instruments) would confidently pan to the right side, the F-05 changed it so the pan was on the opposite side. This in my opinion messed up the stereo image during these parts of a song.

I hear where you are coming from, but using headphone outputs to review a piece of kit isn't that reliable.  You only proved that the headphone outputs were inadequate.  Unfortunately many manufacturers treat headphone outputs as merely convenience features, a box to check. 

Luxman is a good example of this.  Among the very best integrated amps out there for build quality and sound quality but, unfortunately, the headphone output (per reviews) is driven directly from the main amp, via resistors.  So, very high output impedance.   Fortunately I never use headphones in the same room and if I did I have the output from my Mytek Brooklyn to use, whose headphone outputs are said to be outstanding.

Lastly, I've never heard an Esoteric setup that made me stop and listen.  😁