In any civil rights case, the courts must weigh the rights of citizens against the government's legitimate interests which are furthered by violating those rights. As the question points out, the government has a legitimate interest in preventing crime and catching criminals. So why (in America) is the right against unreasonable search and seizure upheld?
It is upheld for the same basic reason other rights are upheld - we do not want to live in a society where they are not. Following the logic in the question, the government ought to be able to enter a person's home or business whenever they have a "hunch" that that person has illegal goods or is committing a crime, whether or not that person is a politician of an opposing party to governor or a journalist writing an expose on the corruption of the local mayor. If this sounds extreme, know that it was law during the mid 18th century in the American colonies, except without the "hunch" requirement - customs officers could be granted "writs of assistance," which allowed them to enter any place where they believed smuggled goods were being stored, without consideration for damage caused by the search. These were so frequently abused in the opinion of not just the Founding Fathers but most lawmakers in the Union that a person's right against searches without particularized warrants was enshrined in most state constitutions as well as the US Constitution.
As a society, there is some agreement that a person can expect greater protection against search of their land property than their person while in public. However, in practice, Terry stops are often accused of abuses, especially racial profiling. For the most part, society agreed ~70 years ago (or more, if you count from the 14th Amendment) that the police should treat all people equally under the law, regardless of their race, because it is unjust to be treated differently by the police due to race. As alluded to earlier, causeless or non-particularized stops are more generally a tool for a government to oppress, by making people fearful of retaliation in the form of stops if they draw the ire of the government. Even a Terry stop can cause a person to be fearful of more altercations with the police when they go out, and can damage their reputation if another person sees them being stopped and assumes they are a criminal. So, the courts, in weighing the conflict between the agreed-upon right of the people against unreasonable seizures, and the legitimate interest of the government to prevent crime, have to decide at what point a search is "reasonable." The "hunch" standard proposed by the question is effectively arbitrary and easily abused. The standard of "probable cause," which is the standard for an arrest, is considered to hamper the government too much. So, for the government to effectively carry out their responsibility, the standard for just a stop is set to "reasonable suspicion," which attempts to strike the balance between the rights of the person and the interest of the government.
This is why it is required of the government to articulate their suspicion for a stop to be admissible - the court has to understand exactly what factors led officers feel they had reasonable suspicion to stop a person, in order for the court to throw out evidence if it believes reasonable suspicion was not articulated for its admission. I point this out to show that as a society, we have not just agreed that the government must uphold civil rights, but that it is more important that civil rights are upheld in accordance with the law than that the government is able to use evidence gained by unlawfully violating rights against an alleged criminal, even if that evidence is damning.
To sum this up, while Terry stops are not the most damaging form of seizure, they can still be used to intimidate and oppress people and populations by the government. The courts have recognized this and require the government to articulate reasonable suspicion to justify a Terry stop - less than the probable cause or warrant requirement for an arrest, but still a standard to prevent arbitrary stops of any person.