I'm going to be very annoyed going through this job application process only to get this email in response 3 weeks later
What is it that you are so annoyed about.
I just think that it is funny that it took them this amount of time to finally respond to my application.
It sounds like it would be very annoying to have to wait that long. You are fine to be annoyed by waiting 3 weeks to hear back about the job.
I'm also mad at them because they missed the deadline.
Getting mad at people for delayed responses is completely rational, however it does make more sense if you had a deadline. If you told them about your deadline and they still responded late than this is even worse.