Tang did claim Han descent in male line (from Laozi no less). But their powerbase was NOT in North China plain.Haha, um, about as not-wet as the Sahara is. The Tang, like other Han Chinese dynasties, had their power base in the settled agrarian peoples of the lush North China Plain, and to a lesser extent among the valley peoples of the Yangtze drainage system and southern Chinese coast (ever wonder why Mandarin and Cantonese are so different? Basically all the Chinese south of the North China Plain descends from a different set of branches of Sinitic from the northern variety). The nomads typically lived in the northwest of the plain (in fact, the Great Wall is basically a failed attempt to erect a defense against those peoples) and were generally either rivals of the Han states of north China, conquest dynasties of part or all of China (the Jin even took the plain, then got fucked up by the Mongols, then came back 400 years later after rebranding and took over the whole country), or client governors at times.
The capital of Tang (and Sui) was in Changan, in Shaanxi. And the home of Li family was in Longxi commandery... which is in Gansu.
Settled agricultural people, yes, But settled agricultural people on the border of the steppe, where they are used to mixing with nomads and trying to make them clients. Tang founder Li Yuan´s mother was a Xianbei, not Chinese (and his father, who had been Chinese, died when the boy was 6).
Compare with Han, Song or Ming, which did originate in North China plain.
Northern Zhou called itself a conquest dynasty. Sui and Tang did not. But which dynasty was best placed to actually conquer Eastern Steppe?