Why did Tang Han's country become so powerful and marry a princess?

Because their ultimate goal is to destroy the enemy, and marriage is just a delaying tactic. For example, in the Tang Dynasty, the affinity with Tubo was to attack the Turks with all one's strength. Or make friends with a country close to you, you can temporarily accumulate strength and eventually destroy each other.

First of all, affinity can save our people from the suffering of war, and it is the people who suffer from war in the end. And make the whole country recuperate and relax the enemy's vigilance. In short peace brought about by peace, we can vigorously develop economy, military and commerce. When the economy develops, the military expenditure will be settled. When the army is well trained, it can win many battles on the battlefield. So getting married is just a plan to delay the war, in order to completely attack the enemy in the future. For example, in the early days, the big man was pro-Xiongnu, and when Emperor Wu of the Han Dynasty fought back in an all-round way, Xiongnu was defeated.

Secondly, intimacy can turn an enemy into a friend, which is beneficial in a short time. When the Tang Dynasty approached Tubo, it was safe to crusade against the Turks. As an ally of the Tang Dynasty, Tubo could not help the Turks, making it easier for the Tang Dynasty to defeat the Turks. However, if Tubo befriends the Tang Dynasty, the culture will gradually be sinicized and eventually become a native of the Central Plains. In the Tang Dynasty, Tubo could become a vassal with a single soldier.

In fact, intimacy is just a way. If you can achieve your goal by other means, the ruler will spare no effort to do it. And the price paid is small, but a lot. Marriage has brought temporary peace to the country, but it is not a long-term solution after all. The ruler had to find other ways to balance foreign enemies, otherwise the sacrifice of kissing the princess would be in vain.