How would you write this correctly? They are not direct quotes.
You may ask yourself, "is this worth it?" or "why is this happening?"
Would you put a period at the end?
Generally speaking, you do not include additional punctuation after phrases within quotation marks that conclude with punctuation.
As usual, there are exceptions. For example, if you wrote an article, "Why Do People Vote?", then you must use the question mark (as I just did) as a component of the title and it must be ignored, thereby requiring the use of the comma. Indeed, when quotation marks are used to identify a title you cannot move punctuation inside the quotation marks as it is not part of the title. For example, "I read 'I Voted', but it was dry reading."
If, on the other hand, that same quoted phrase is a quotation (rather than an article title), then the punctuation within the quotation serves as the comma. Thus, if you write, "why do people vote?" you do not place a comma after the closing quote mark.
And just to prove how fun English is, I believe there is an additional exception for when the sentence ends with the same punctuation mark. Thus, even if we use the article title, above, we would not write, why would anyone read "Why Do People Vote?"? Instead, we would write, why would anyone read "Why Do People Vote?"
I'm likely to get torn for not providing a lot of documentary evidence for this. C'Est la vie.