Why did the Israelite captives from the northern tribes not have to come back?

The northern tribes had continually migrated south into Judah, so at the time of the captivity, the Israelites were already represented in Judah. Therefore, the captives did not need to return, since all Israel was then in Judah, at least representatively.

Les explains that the northern ten tribes had been so depleted in numbers that they were like "two little flocks of kids" (1 Kings 20:27). Because of a constant migration of Israelites from the northern tribes down into Judah, the people taken captive did not have to come back. As Les points out, all of Israel was already down in Judah, at least representatively. He confirms this with 2 Chronicles 15:9, showing that the migration had already brought the northern tribes into the southern kingdom before the captivity.

2 Chronicles 15:9

And he gathered all Judah and Benjamin, and the strangers with them out of Ephraim and Manasseh, and out of Simeon: for they fell to him out of Israel in abundance, when they saw that the LORD his God was with him.

Why did the exiled northern ten tribes not need to return from captivity?

The exiled northern ten tribes did not need to return from captivity because a constant migration had already brought Israelites from the northern ten tribes down into Judah. By the time of the captivity, all Israel was representatively in Judah, so a return was unnecessary.