Health,
Are you quoting a different Shulchan Aruch (maybe Shulchan Aruch HaRav)?
In the standard Shulchan Aruch by the Bais Yosef, Even HaEzer 1:13 says that woman are not mechayavot in pru u’r’vu. The Rama says that some say that she should still not remain without a man because people will be choshed her. The Be’er Heitiv says for a woman getting married is a reshus, and this Rama is based on eitza tova.
Zaken and Yalda are not specific terms with specific meaning they are general terms. The point of marrying someone compatable with you is to avoid fights and discord in the home. Zaken and Yalda in the gemara are just an example of something that would cause discord.
You are correct that the Shulchan Aruch appears to give a different reason than Rashi on the Mishna, but that mishna is the listed as the source. I can think of a teretz but I would like to look into it further.