Is it usually worthwhile to argue to try to convince someone?
Plenty. The elaboration likelihood model compares the efficacy of persuasive argument under various conditions – this wouldn't be worthwhile if its efficacy were zero. Attention plays an important role: if an audience is inattentive, the semantic content of an argument may matter less than other factors involved in persuasion.

Reactance is also relevant in that arguing with a particularly resistant audience may result in even less compliance and more opposition. This has been studied empirically. It is also not universal; reactance varies with personality and other developmental factors. Thus both compliance and resistance exhibit variation empirically – enough to make persuasive argumentation viable with some people some of the time. This conclusion is also the corollary of a popular (if unscientific) aphorism:


  You can fool all the people some of the time and some of the people all the time, but you cannot fool all the people all the time. — Paraphrased from Jacques Abbadie