I'm not saying this explains the number at all but it got me thinking. If I want to do the achievemnt for MIN/BOT of gathering 10.000HQ I want to do that where I have the highest & chance of getting HQ. I think the highest without any buffs is 15% which would mean I need to collect about 70.000, for example maple logs. The added benefit of this is that I could then use those to get the achievment for crafting 10.000 HQ carpenter recipies.

Obviously there are other concerns such as making gil while doing it but in terms of pure speed I would probably do items like these which could explain a fraction of it at least.