Just last week I had a couple fruitful interactions with applicants during the rejection process. I got this from a prospective intern;
Thanks a lot for getting back in touch. I have spoken to other companies who have decided that I was not right for them this summer and they informed me of this by just never getting back in touch with me. So I really appreciate your email.The intern wasn't right initially but in I've learned more in subsequent exchanges that might make him a good fit. If not this year, it will be next year! Furthermore, he is helping make an arrangement with his school program that could serve as a funnel for our internship program. Another unsuccessful applicant passed along a friend of hers that is a better match who is also considering a new job.
Yes, responding to every applicant is overwhelming and seemingly impractical, especially when a large percentage of applicants are irrelevant and just spamming their resume to employers. However, you can use a (free) ATS Applicant Tracking System to take care of this for you. I generally have a template decline email reiterating the key aspects of the job, explaining that we've had lots of applicants, they weren't the best fit, and that we wish them good luck. Boom, you write it once and use it over and over with a click of the finger as you review resumes. It also gives applicants a chance to get back to you if they are tenacious, and actually do fit the job well.
Reply to the people wanting to be part of your team. It's practical - you might find a match after all. It's branding, it's manners, it's relationship building! Try it. You might like it.