should I put "the" preposition before "citizen's life" ?
Viewed as a whole, I believe that not only is allocating the income of taxes to art worthless but also governments should make more efforts to bring artistic crafts into [ ? ] citizen's daily life.

And what can I say instead of daily life?

Question

should I put "the" preposition before "citizen's life" ?
Viewed as a whole, I believe that not only is allocating the income of taxes to art worthless but also governments should make more efforts to bring artistic crafts into [ ? ] citizen's daily life.

And what can I say instead of daily life?

Answer

(1) "citizen's life" = the life of one person
In this case you need to say " a citizen's daily life", with "a"

(2) "citizens' lives" = the lives of many people, talking generally
In this case, no preposition.

I think you mean to say sentence (2), and this sounds more natural English.

Also note:
"income taxes" not "the income of taxes" (and you could simply say "taxes", doesn't really matter which one)

Answer

No need to put in the preposition "the" it sound corret the way it is. If you put on the preposition "the" it sounds like you are talking about a specific citizen.

Instead of "daily life" you could say every day life.

Answer

"The" is a definite article, not a preposition.
I would say,  "into citizens' daily lives." or "into the daily lives of their citizens."