Some developers like to establish a relationship directly with their users, not pay (in dollars, or advertising) a middle-man like GitHub, GitLab, or an App Store.
But look at it from the other point of view: how does a non-technical user determine if a binary download is malicious?
And how, then, does Google/Microsoft/Apple protect those users from their ignorance?
Given that the internet is full of people attempting to get non-technical users to download malicious software, often my mimicking exactly the sort of site the OP has created, then is it really practical to insist that Google/Microsoft/Apple allow the OP's site to download software to a user's machine freely?
The advantage of the middle-man is that it acts as a trust agent (not necessarily well, of course). If you download a malicious binary from an App Store, that is the App Store's fault for letting it on there in the first place.
Sure, you need some kind of middle-man as a trust agent, but Google/Microsoft/Apple are not the only possible trust-agents, and their model is inherently biased towards certain useful software production models.
Let's say I keep bees as a hobby, and I write some small piece of software that tracks and calculates something to do with honey production. I post it to my favourite bee-keeping forum, other people try it and like it, and when a new bee-keeper joins the forum they're often advised by forum regulars to try my software out too.
That kind of software can be a huge help to people, but it's not a good fit for an appstore because it's never going to turn a profit, and at least on Apple's store (with the $99/year publishing fee) it'll drain money quite predictably and regularly.
A bee-keeping forum will never be trusted by as many people as Google/Microsoft/Apple, but the people who do trust it probably trust it a lot more.
You could simply host the binary on GitHub and GitLab and have the link on your website point directly to it. The user would never know, so you'd get the best of both worlds. You develop a direct relationship with your users without paying anything forward to GitHub or GitLab.
With that said, hosting the binary on those platforms won't necessarily help as Google can flag individual repos according to some other comments here.
Every indication I've read is that simply linking to the binary download, even if it's offsite, will be enough to flag the page hosting the link. So I would have to link to an alternate site hosting the link, and risk that page being blocked instead, and then I'm right back where I started.
I would, if at all possible, prefer to find a solution to this problem so that I can directly host my software.
If you prefer to directly host it then you will have to wait (and hope that no one files a complaint about your domain).
At some point your domain will have a sufficient score and it will not show the warnings to users.
How long that will take is, however, outside of my knowledge and it would be nice to have some official reference about it; as it stands I agree with you that it feels like begging to a benevolent dictator.
The point is that these warning still appear for executable downloads from Github (at least they did a few years ago when I independently thought of this as a workaround) - my guess is that Microsoft and Google are using some kind of unique'ish binary fingerprint, such as Imphash or SSDEEP (in conjunction with other signals, such as domain age, digital signature etc)
