As has been said, there is no way to make everyone happy. I think that preorders would only work for some games; usually only highly anticipated titles, and that it would only be successful in limited (no pun intended) scenarios. A better solution would be getting publishers and developers to agree to higher print runs. Limited Run Games releases aren't as under the radar as they were when this started. Disc and cart counts should be adjusted accordingly. This would at least help get physical copies into more of the hands that want them for the reason of having and playing them. Unless you're just buying something because it's guaranteed to be rare. In that case you don't really have an argument to stand on; first come first serve.
A large chunk of the frustration over missing out on physical copies of games should be directed at the game publishers themselves; especially when you consider that we're receiving absurdly priced special and/or collector editions that include a bunch of keepsakes and a digital download code. It's insulting actually. All of that effort on the Battle Garegga special edition and it doesn't include disc. Though Garegga might be more well known in certain circles, I would argue that it's just as niche as many of the games that LRG has had pressed. We are looking at a similar scenario with the upcoming Sonica Mania. The preorder window would likely work even better in these cases, with massive organization like Sega behind them. I imagine it wouldn't be too difficult for them to pull Amazon preorder numbers to send to Sony/Microsoft/Nintendo to press wantever amount comes out on the other end.
There's no excuse for the lack of a physical version if the demand is there. Smaller or less expensive prints are not only a thing, but they seem to be kind of common this generation. I'm looking at my shelf right now and I see Caladrius, two different region copies of Leynos, Earth's Dawn, Shantae 1/2 Genie Hero and Gravity Rush Remastered. These are all lower priced releases, most of them b-tier. Call it anecdotal, but I was able to walk into a local brick and mortar and pick up half of the games in that list. One of them was the result of a goddamned kickstarter campaign!
Sorry, this post became more about the lack of physical media than an additional a contribution to the Limited Run Games topic. Though the rise of digital only distribution and the industry's attempt to shove aside physical media is why most of us are here.