Fortunately, if you send no referer it seems you get the image directly. This is easy to do with a browser setting.

On your desktop browser yes. On mobile devices not as easy.

And even on desktop you might not want to globally disable sending referer because other sites might break.

And even if you use a browser add-on to only block referers for i.imgur.com, most other people haven’t so everyone else is still being redirected.

What's even worse, on mobile, imgur heavily downscales and compresses images. Which is fine for kitten photos, but completely destroys any of its utility for screenshots, as you can't read normal-sized text on the phone.

But running an image hosting service that anyone may post to is a lot of work.

Firstly you have your run-of-the-mill DMCA takedown notices, both the legitimate and the bogus ones. So you need to deal with those. And if you are unfortunate with your choice of hosting provider or registrar then those might not forwarding DMCA takedown notices to you as they should but instead just terminate service.

And DMCA takedown notices aren’t even the worst part. Sooner or later someone might post illegal photos to your server depicting sexual abuse and other atrocities, and you absolutely need to figure out the proper procedures for dealing with that.

On top of that you have trolls abusing what ever form of report functionality you create.

This leads to a kind of Catch-22. You need for reports to be legitimate in order to provide service to the honest part of your user base, but at the same time you neither can nor want to look at the worst kind of images that someone could post.

So you need systems that can automatically identify those sorts of images without human interaction. And certainly it will be very difficult to get such a system correct so that it has no false negatives and limited amount of false positives (the latter meaning that the system removes images that shouldn’t be removed), because once again you neither can nor want to look at the images that it should be able to identify and remove.

Obviously, it’s not impossible — otherwise there wouldn’t be any image hosting sites in existence — but like I said, it’s a lot of work.

Additionally, even if you do get all of that right, the utility of a HN specific image hosting site is very limited. For example, if the HN community was to adopt it then suddenly the referer check that was there to make the service feasible in terms of bandwidth cost and server load will result in seemingly broken links for anyone on HN that wants to share any of the images outside of HN.