Actually there is a feature that will allow anyone to upload a link to anyone else's image or tutorial or whatever kind of resource. However, if you only upload a link to something, it doesn't have a thumbnail so that you can see what the image is. You have to follow the link to be able to see it. So far, I haven't understood the need for this type of upload. But it's possible, if you want to use it.
Images get to be on the front page of the gallery because they have been marked as Favorites, more than any other images. (If you're registered and logged in, you'll see a little star icon for marking something as a favorite.)
There's currently no way to request special billing. Although I think it has been discussed the possibility of having something like a Featured Images section, or something like that. But I don't think it's ever moved past discussing as possible.
I think it's a shame that more people don't look through the older gallery images, because there are many which deserve to be on the front page. But they can only get on the front page if members mark them as favorites. It's just that apparently not many people are interested to sort through the entire gallery, now that it's gotten so large. And unfortunately, people are voting only on that first page of images, and the great ones that live further back, are probably never even seen.
Yes, the image you gave a link to was an About screen contest entry a few years ago. I don't think it was the winning entry, but was the runner-up. I think there's a good chance that a lot of the images you want to see might already be there. That one you linked to is there. You just have to look around or search around to find it. You could try searching for the artist name, to find out if they might already be uploaded. (Although if the artist doesn't use their real name... Well, just a thought.)
To be honest, I think you have a valid point. I had made a feature request a couple of years ago, when the gallery was still brand new, to have the front page, or first few pages moderated. In the scenario I imagined, moderators would choose the best images, and perhaps rotate them around, so the gallery doesn't get stale. But it hasn't really worked out exactly like I had imagined.
It would be reasonable to make a feature request, even if you don't know exactly how it would work. Just requesting that some way can be found so that all the many great images which are hidden, can be rotated to the front from time to time, is a reasonable request. If you'd like to make such a request, you can create a New Issue on gitlab, where the project's...I think the entire repo is there now. If I copied the right thing, this should be a link to open a new Issue:
https://gitlab.com/inkscape/inkscape-web/issues/new.
Part of the problem for me, in marking images as favorites, is that once they are marked, they become part of your profile. And personally I don't want to clutter up my profile with 30 or 40 favorites. I have thought that I might register another account (with different email) and uses it only for voting favorites. But just one more person voting won't have much effect.
Like Inkscape, Inkscape's website is work-in-progress.