I feel like this is indicative of one of three scenarios:
1) For whatever reason, there is a high turn over rate at your company. This isn't always a bad thing, but if a company is always hiring, it's usually because they are consistently losing people as well.
2) You are experiencing crazy explosive growth, so much so that every month you need to hire more of the exact same positions.
3) The requirements for the job are poorly defined. This would lead to a lot of people (mistakenly) applying to a job that they have no hope of filling the requirements for.
Whatever the case may be, I really think the only reason you guys are getting any kind of backlash is just because it is becoming a common theme to apply to DeviantArt and never receive at the very least a "Sorry, not what we're looking for". Do it to enough people, and there's bound to be a response.
EDIT: There is a 3 month period in which 20% of new people get fired?! No wonder you are always hiring. You are effectively telling people to leave whatever job/security that they have, then cutting a non-trivial amount of them loose because they weren't a good fit? That's not their fault, thats a problem with the hiring process. Who knows what it does to the moral of the other workers. Oh wait, they are all remote. No one ever finds out...
That puzzle you mention in your post, would be a great way to give people an example of the kind of problems they will face before they choose to apply.
3. we get very few off-topic applications. most who apply do have some level of experience to qualify for the position. yes, the first screen is subjective, and we clearly make mistakes if all we have to go on is the CV without a single link to one's work. Thats why the position description suggests submitting code samples like a link to the github account would be very beneficial.
we do respond with an automated message acknowledging the receipt of the application and it spells out what to expect. We contact again to request code sample and exercise of those who pass initial screen. unfortunately sometimes those emails get trapped in spam filters. We did used to send rejection messages in the past, but this also did not work very well because many applicants expected very personal response and coaching on what went wrong. As all of us are also full time developers, we just dont have bandwidth to do that. but based on your guys's comments we'll see how we can do it again.