Women tend to want the best outcomes for their children, so will choose the sex with the much higher quality of life. There would need to be powerful personal motives to choose the lower status sex knowing their baby will have a much harsher, poorer life. Asking people to forego personal gain for the long term good of society doesn't work. We'd all be vegan and take the bus/cycle and donate much more if we were that selfless.
There are only so many managerial positions available. A lot of what makes society work is time-intensive drudgery. Whether the child is male or female would make no difference in quality of life if that child spends a lifetime working the fields. And yet, fields must be worked. Mines mined. Horses shod.
I'd say there's also an odd assumption in thinking that just because women have special value in a society, the men have much less value. The women in this proposed society are valued for a) childbearing capabilities, b) magic use, and I suppose, c) "more rational and clinical" thinking. Putting them in the fields to work, or the mines, seems anathema. But these other roles in society are valuable, particularly for the families who would benefit most directly from having manual laborers within the family. They could choose to produce only daughters; but if they hold no expectations of having their daughters govern, lead a business, etc., or be paid highly to participate in magic rituals for defense, there'd be no special impetus for having only daughters. A family that has worked the mines for generations and earned special status within that milieu might well already have a family tradition of producing mostly sons. Not to mention that there could be a negative stigma for a family that puts only daughters in the mines: As if, that's really a waste of daughters, anathema to the principle value of females, and possibly (depending on the society) a kind of blasphemy.