The phrase 东北人 has been widely used by native speakers but 西南人 is not as common.
Is it not equally correct to say 西南人?
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As a 西南人, I have to say that it is rare to hear. 南方人 (Southerner) is okay.
If someone is from the south side of the Huanghe River, they would let you know which province they are literally from, like Sichuan, Yunnan or Guizhou.
I suppose the reason is dialect, which so different in southern China.
But 西北人 (Northwestern) is commonly heard.
西南人 is a rare expression. Few people say like that, so it sounds weird. Grammatically speaking, it is definitely correct, and it refers to people from Sichuan, Guizhou, and Yunan.
By the way, there was a famous university in Yunan Province, named 国立西南联合大学 (National Southwestern Associated University).
The local dialects in Sichuan, Guizhou, and Yunan, are linguistically classified as 西南官话 (Southwestern Mandarin).