(Procreative Axiological Asymmetry): While it would be bad, or undesirable, to bring a miserable life into existence, it isn't good, or desirable, to bring an awesome life into existence.
in order to secure
(Procreative Deontic Asymmetry): While we are obliged to not bring miserable lives into existence, we are not obliged to bring awesome lives into existence.
PDA is certainly very intuitive. There seem several routes by which it could be defended. Adopting PAA to this end strikes me as a particularly odd route for defending PDA. In general, the inference
(No Duty → No Good) We shouldn't be required to do X, therefore there is nothing good about X
does not seem a particularly appealing one. It would be more than passing strange for a convinced opponent of Singer-style duties of beneficence (for example) to try to ground their view by claiming that the welfare of people in developing countries just doesn't matter. Surely one does better to grant that there are genuine (pro tanto) goods at stake here, but simply insist that the associated reasons for acting aren't requiring reasons -- perhaps because granting such reasons "requiring" force would be too costly -- interfering too much with our moral liberty to live our own lives, or some such.
And isn't that also the better way to defend PDA? A duty to procreate would be incredibly intrusive -- surely if any putative moral demand can be disqualified on the basis of being "too demanding", this is it! What's more, even from a simple act utilitarian perspective, it doesn't seem particularly empirically plausible that constantly churning out more kids is really the best means available to you for improving the world. That is, compared to more traditional demands of benevolence, the procreative demands ruled out by PDA would both (i) be more intrusive/demanding, and (ii) bring about less value/benefit.
PDA thus seems on pretty safe ground, without any need to resort to PAA. We can grant the commonsensical axiological claim that it's a good thing to bring into existence people who will go on to live awesome lives -- awesome lives being, after all, amongst the best things the universe could possibly contain! -- without being forced to unpalatable conclusions about duties to procreate.