I actually think they're terrible examples because you're not comparing like for like...
Was using the same dates of the 8th and 16th August so while a limited sample size it is like for like on those days. I used SIN TYO and DPS because they are city pairs that at least have some level of competition on them. It would be pointless comparing cozy duopoly routes with only the home aAustralian carrier and the home foreign carrier such as PNG or even NZ because with only two carriers capacity and airfares tend to converge on a what the market can bear, rather than any competative forces. In a lot of cases with BNE - foreign carriers are absent at the moment eg: Thailand and/or the "home carrier" of Qantas is absent and only available via SYD
For that exact day you've mentioned comparing non stop (non low cost options) BNE wins with a slightly cheaper QF option. However on average it's about $200-300 more from BNE which is clearly a lack of competition, BA from SYD seems to force QF to match (or often beat) the non QF1 flight option out of SYD.
Agree, that on that particular day BNE-SIN return is cheaper on QF than SQ and as you say, on average the BNE-SIN fares are more expensive than SYD-SIN return fares, because of the competition from BA and from JQ that is present in SYD and absent in BNE.
Also an unfair one given Chinese carriers often dump cheap capacity into the market.
The Jetstar options out of BNE are cheaper (and will become even more so once direct flights start in Oct/Nov) and the next best full fare (non China option) is Cathay (assuming we don't count VA) where both BNE and SYD are about the same.
Its not about fairness, the Chinese carriers do exist and they do dump capacity on that SYD-TYO route (and indeed dump capacity into a lot of markets and they sure arent desireable or indeed preferable for some people but they do represent competative fares that keep other carriers on their toes), again, because there are more Chinese carriers serving SYD rather than BNE, added to the fact that two other Japanese carriers also serve SYD, and not BNE at the moment, then it makes sense that these competitive pressures would make SYD-TYO fares cheaper than BNE-TYO fares (I am combining HND and NRT as "one market" TYO for comparison purposes). Your point about once JQ begin BNE-TYO services is also correct, and that will alter the capacity and the market forces, obviously VA's new one-stop service via CNS will not have enough capacity to radically alter the market, as its more of a slot squatting/co&*k blocking QF exercise, rather than a logical or even viable route decision.
I feel like public holiday on the 16th might be inflating BNE prices... using a 6 day trip on Google flights showing the cheapest result round trip:
Didn't realize that there was a QLD public holiday on the 16th, my bad, point taken, the Bali market yield curve is entirely dominated by state school term dates.
I think we are agreeing with each-other mostly

, increased competitive pressures from LCC's, other third party airlines through their own hubs, or other international carriers, such as BA and EK, all affect the capacity and the competitiveness of city pairs and markets. Because SYD has more international carriers serving it than BNE, it makes logical sense that there are less competitive pressures in BNE than in SYD.