As the cover letter increases in importance, will there be a time when people will not bother to write a résumé? Why or why not? Justify your answer.

No.

Explanation:

They will not be a time when people will no bother to write a resumé. Basically, because the content of the resumé is way more important, that information is the reason of writing a resume in first place.

Despite people's likes or dislikes about the cover, it's not the purpose to have a cool cover letter and no info. If people start changing these priorities, they won't get any job, for example.

I do not think so because a resume will tell someone what this person has done so far. The cover letter is just to make it look nice and to not reveal to anyone else what you do or any personal information. A resume is more important than a cover letter.