The chart near the end, around latest hardfork, shows that increasing interest on HBD has strong correlation with raising hard cap price - something witnesses should be taking into account.

Correlation != causation likely applies in this case. I say this as someone who has observed in real-time many of the potential factors that could have caused previous rallies in HBD price.

But witnesses are well aware of the potential for the interest rate to influence the attractiveness of HBD, which tends to increase the price, which creates Hive->HBD conversions to profit from that price. But the Hive->HBD mechanism tends to also increase the price of Hive, which decreases the chance for Hive price to actually hit the hard cap price.

And pragmatically speaking, it is fairly obvious that most HBD is being bought and held by people who have little knowledge of the workings of HBD, interest rates included. In the future, of course, interest rates play a larger role in determining HBD supply, once more holders are aware that there is a potential to earn interest on HBD by keeping it in their wallet savings account.

I feel like I'm still missing one important piece of the puzzle.
However there are two other places where hard cap price rises: near 13M mark (HF19) for a short time followed by period of steady price and later between 19M and 23M (all before HF20). Such rise of hard cap price can only be caused by either falling supply of HIVE (did not happen as we can see on bottom chart) or raising supply of HBD (not visible as spike in virtual supply because in the same period market price was very high).

Pretty much every crossing of hard cap price for Steem occurred because 1) Steem price went up a lot and a lot of SBD was created as a result of increased inflation (which raised the hard cap price due to increased supply), followed by 2) Steem price dropped a lot.

All this gets back to @smooth 's point: hard cap price going up isn't a problem as long as Hive price goes up as well. From the blockchain's point of view, HBD acts a bit like a convertible, interest-paying debt. And it generates it for similar reasons: it expects to have a higher internal rate-of-return for Hive's price than it offers to HBD holders, at least over the long haul, so the blockchain pays for stuff in debt in many cases instead of Hive. So far, this bet has definitely paid off for the blockchain.