Yep, nobles can only marry other nobles, the commoners become concubines. Same, the children of concubines cannot inherit titles, but the legitimization of bastards is very common in Aetas due to the situation.
There's a little problem with killing anyone who complains: if you kill the wrong one, you end up with their entire armies against you. Or worse, someone like the Queen, Gods forbid. And the first to complain would be the church of Ishtar, which perform weddings and is the most revered of all the clergies.
It is part of the lore of the world I created and was put there to give more depth to it. And also because it makes sense. It, for example, reduces the risks of the bloodbaths that can happen when a ruler dies. See what happened IRL with the sons of the Sultans of the Ottoman Empire.
The MC though does not care very much. But yeah, legally, wives do take precedence over concubines, who are higher in the "food chain" than the slaves are.
Now, some of the Mc's lovers will be raising in rank because of the feats they accomplish.