Note that AKG specs their headphones in "dB/V" not "dB/mW" - it lets them get bigger numbers out of the same spec. The K7-- series are fairly low sensitivity for a dynamic headphone, and not long ago were revered as some sort of unslayable beast requiring at least 1.21 jiggawatts just to make a quiet little "burp" happen (so maybe there's some hyperbole in there...). Here's Tyll's measurements of the K7XX (if you meant another 7-- series family member he's got those too) -
https://www.innerfidelity.com/images/AKGK7XX.pdf
Showing .64 mW (and .206V) to reach 90 dBSPL at 66 ohms. That's "somewhat worse" than a lot of other dynamic headphones. It isn't "unslayable beast" by any means (and unless AKG has revised things heavily with the 712 or 7XX, these still have a maximum rated input of 200 mW), but it does require more power than is typical (especially vs more modern designs that target mobile use heavily). A decent headphone amplifier should be able to do at least 10 mW/ch though, which is enough to get you up to around 102-103 dB (I'm lazy so that isn't dead-to-rights on the numbers), and may feel a bit "stretched" for dynamics depending on what you're listening to ++ how loud you want to listen. More robust amplifiers tend to have no problem with 100mW+ which will easily get you to 110 dB without much fuss. So a lot of amplifiers can probably drive these just fine (and from when I owned K701, I never encountered a dedicated headphone amp that had issues with them, but some portables, and some built-in headphone jacks weren't as happy to see that load vs something with higher sensitivity, like Grado or Denon headphones).
So what about the receiver? Who knows. The specs you've provided mean absolutely nothing in the context of this question, and its likely Onkyo A) doesn't provide headphone output specs and B) the headphone output isn't actually tied into the main amplifiers (its likely running on its own separate op-amp/chip-amp circuit so that it can be cut out from the processing feeding the main amps). All isn't lost there, but there's a chance that it isn't "great" as a headphone amplifier (e.g. very little power out, maybe weirdness with impedance, etc). On the other hand, it might be pretty good (no joke my second favorite dynamic headphone driver is part of a 60lb+ integrated amp - so yeah "they're out there" but there was literally NOTHING in that amp's specs about the headphone amp (I ultimately gave in to curiosity and opened it up and learned its a dedicated, op-amp based circuit that sits after the pre-amp section) so it was a completely unknown quantity from its documentation). But we just don't have the information to know, and a lot of "headphone centric" review sites really don't seem interested in talking about hi-fi gear with built-in headphone jacks or anything that isn't "desktop hi-fi" or "personal audio" these days. As far as "better" that's an entirely different discussion, because that's value-weighted (e.g. you're asking us to tell you what you'll feel).
Some things I'd potentially wonder about with a receiver (because I've had issues with this in the past):
- Noise floor. A lot of hi-fi/speaker components don't worry about noise floor as obsessively as headphone audio components, mostly because the sensitivities on speakers (and the distance from the listener to them, and the room's noise floor, etc) are a lot lower, so you don't have to worry so much about getting rid of hiss. So if there's background hiss/noise when listening to your 7XXs, that's a good indication the noise floor is relatively high (and that background noise should be expected to get worse with higher sensitivity models), and a dedicated amplifier may alleviate that (why "may" - because not all dedicated amps are created equal).
- Channel balance. If the volume control isn't done awesome, and the gain structure is wacky, its conceivable that you may have an obnoxious scenario wherein the left or right channel plays louder than the other at the volume level you'd like to listen at. This can be the case with some dedicated amps too, but again if that's a problem, you may want to consider another amp.
- Power draw/waste heat. A lot of AVRs (especially newer ones with more computer stuff in them) tend to use a good deal of power just to be "on" - like 80-100W or more. That's pretty wasteful (imho) when you're just driving headphones, and beyond that it may lead to extra heat in your listening room that you didn't want to deal with. By contrast some headphone amps are extremely efficient, and you can easily get into sub-10W equipment that will drive your headphones painfully/dangerously loud. Or go nuts with Class A devices that still don't use that much power in absolute terms (e.g. a Class A headphone amplifier may draw 40-60W - that's "a lot" for what its doing, but 40-60W is not "a lot" compared to some appliances in your home, and that's heaps better than dealing with an AVR or a Class A speaker amplifier).
Something you could do to investigate this a bit without buying anything - try plugging the cans straight into the Dragonfly (its meant to be a headphone amp too), or into other devices you have with headphone outputs, and listening if there's any big differences with the sound. See what you think. If something sounds "a lot better" then maybe the Onkyo isn't the best candidate. If you end up still liking the Onkyo after trying comparisons with some other devices, live happily ever after with it.
EDIT - Guess I waited forever to hit "reply" and you replied more, so I'll reply some to that:
