Does it make sense to write cover letters ?
Yes, but ONLY if it's the right cover letter. There is an astonishing amount of confusion of what a resume and a cover letter is for.
Resume: This is describes you and your professional history. Your experiences, skills, achievements typically by going through your education and work history in chronological order. That's who you are. It's the same for all jobs you apply for since you are still the same person
Cover Letter: connects your resume to the job description. Why is this a good job for you and why are you good for the job? A good format for a cover letter is to go through the requirements in the job description one by one and match them against line items in your resume. A cover letter is individually tailored to each specific job since every job description is different. A good cover letter shows that you have done your homework, researched the company and role and that you have a well informed opinion on the job.
A good cover letter can give you a big advantage. In many companies, applications are first scanned by a recruiting staffer who often has little understanding of what the job is actually about. Their job is to match requirements against the candidate, which is difficult. If the cover letter already does they work for them, you have a much higher chance of getting through the first phase gate.
A bad cover letter however can be a problem. Something that's cookie cutter and not specific to the company can be interpreted as you being lazy and not doing your homework or just doing a random blast of applications with no special interest in this role.