I cannot understand why on Earth you’d be sending multiple cover-letters to so many companies doing totally different things. If your purpose is to get a job as a Product Designer (and incidentally make a living), than no job will make you happy. Not even this one you landed on.
On the contrary I could have enjoyed your article more if I saw you tried to apply the design thinking methodology, to get into Product Design. Inception.
So the first thing would have been the discovery process, in which you would have figured out what your purpose is. Afterwards, you should have worked towards nailing that. For example, having a list of companies you apply to, that all try to solve the same problem you’re inspired by. If there’s something you’ve focused on all your life, or something that doesn’t let you sleep at night, which you talk about to all your friends and strangers, that’s the problem you want to work on, at a company that’s addressing it.
Thanks for taking the time to point out the process these companies go through when performing an interview. If you can do update your article, inspiring others to carefully pick where they apply to — in the end, it’s a two-sided process — the companies are being interviewed by you as well.