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That's what they should be doing, but the masses very often have an hard time understanding the concept of a "puppetmaster", the people often claim to know there is someone pulling the strings, but when asked to clearly point out "who it is" they are unable to focus on anything concrete, or come to a conclusion guided by sound reasoning.
So tageting the most immediate and visible symptom of the problem is the most which can be achieves by an angry mass of people with no real organization directing them. But that could still lead to something if there was any close attention to the reactions of who is trying to defend the symptoms, eventually following the reactions could still lead to the root causes.
But any protest with no organization will fail to achieve anything, both for the failure of directing the protest towards something crucial, and both for the failure to take advantage of the created disruption created, meaning no real change after the momentum of the protest dies down.

The revolting people targeting the sources of income of the immigrants is still a good tactic. They are not targeting the people(immigrants) by the systems allowing them to proliferate in the host nation.