Though it's said the flu vaccination is not 100% effective to all people, it is found it can still help to protect elderly from many diseases and prevent them from thousands of hospitalization (actually I want to say this can help government and society to save a lot of resources).
Besides, even the young taken the flu vaccination 100% effective, this would not weaken their immune system, instead can reduce the virus in circulation. Because their immune system may be strengthened to enhance their body resistance to virus and bacteria.
Thus in my point of view, flu vaccination is recommended to both young and the elderly, under the condition that the society or government have enough resource (tax?) to promote and improve the health of their citizens.
P.S. People allergic to eggs are not recommended to take the vaccination, because it is heard some flu vaccines are made from eggs.