Arrest gives them legal authority to search the person of the accused and find evidence of other crime. Perhaps they will find something that leads to a felony and authorization to hold. For instance, you probably wouldn't want to release someone who was heavily intoxicated in public while in possession of a deadly weapon.
To be clear, I'm not saying I'm thrilled about prosecuting people for many of the crimes for which the contraband would constitute, but the advantages of arresting the perp even if they'll immediately be released is obvious.
All that you’ve said is clear Abe obvious and the logic of the post-90s sustained reduction in crime we saw for decades.
The challenge is that holding people accountable for misdemeanor crime, using stops as pretexts for deeper investigation, and aggressive enforcement of nuisance laws all contribute to disproportionately bad outcomes for underprivileged people. That consequence is more directly obvious than the consequences of not going effective police work, which is why our society collectively made the choices it did over the last few years.
To be clear, I'm not saying I'm thrilled about prosecuting people for many of the crimes for which the contraband would constitute, but the advantages of arresting the perp even if they'll immediately be released is obvious.