People can and do become slaves in Seanchan willingly, for the very reason that they can rise to greater positions of power and authority than they could as free men or women. If it was required that to be the highest naval officer of the Empress, you had to become her property, 9 out of 10 high-ranking captains would probably jump at the chance. Since such a promotion would be highly unlikely to come to anyone of less than middle age (contrary to the usual tropes in fantasy of teens and 20-somethings leading armies and nations, unless there is a long, hard & bloody war going on, no one reaches a rank equivalent to general or admiral without putting in quite some time in service of one sort or another), Egeanin's mother almost certainly received her promotion before Egeanin herself was born, and thus Egeanin would not have been born into slavery. Unless there is an issue of attainder, her automatically joining her mother as property seems counterintuitive. Of course, it is possible that there is such an aberrant custom (usually for plot purposes, such as the "Amyrlin-is-automatically-a-full-Aes-Sedai-but-no-law-says-she-must-be-one-first" loophole), but that seems like the kind of thing that would have been explained or mentioned, at least. Absent that, I would have to say that if the Hand of the Empress at sea was required to be property, there is no reason why her children would have to join her in bondage.

All of that is, of course, stipulating for the sake of argument that Egeanin's mother WAS property, which seems unlikely. I do not even recall that it was stated she was even so'jihn.

Anyway, for the Seanchan, slavery (when not imposed as punishment) seems analgous to the status of employment in older times in the real world. There was a time, even in the USA, when being employed was looked down upon. A man earned his own living, from his own land or by buying and selling his own merchandise or by selling his own products. People who sold their labor or services were seen as dependant, and the comparison of wage-employment to slavery, made by the defenders of the latter, actually had some weight. On the other hand, some really good jobs required entering the employ of another, including many government positions. The choice of a Seanchan between the prestige or influence of a high-ranking office which must be filled by da'covale, or the freedom and personal dignity of a free man might be akin to a man who had to choose between the respect of self-sufficiency and the money or power of an important salaried position.