This early classification of kids, for lack of a better term, is so screwed up. And it has all kinds of issues around social background, racial discrimination and whatnot. Ever PISA study I remember basically gave us the same feedback, black on white. Not that I expect it to change in my lifetime so. it did get considerably easier, as opposed to easy, to get access to university level education when starting out at a Hauptschule since I went to school. Back then, like 20 odd years ago, it was basically impossible to do so.
I have the highest respect of everyone who actually goes from a Hauptschule to a university degree, this is probably the hardest way to get higher education imaginably around here.
As a German who got into the highest of the three tiers ("Gymnasium" which has nothing to do with sports in German), I absolutely agree.
The understanding was that if you wanted to go to university, you needed to go to Gymnasium because it was the only way to get an Abitur (basically, a high school diploma) within the school system. Realschule was for those who didn't quite make the cut but they could still switch to Gymnasium later. Hauptschule was the drain strainer, it would effectively brand you as a failure and you'd be lucky if you are even considered for a crafts job if anything.
Of course it's important to keep in mind that this decision is made for ten year olds. They have their entire life ahead of them and some do defeat the odds but the struggle of those barely making it to Gymnasium to stay there (especially if their parents can't afford private tutoring) is real and in order to catch up from Realschule you basically need to put in twice the effort because you need to compensate for the parts of the curriculum you missed out on in addition to learning the new stuff. If you end up in Hauptschule, being able to switch to Realschule is usually the best you can hope for in order to dodge the stigma. And of course Lord help you if you have any kind of special needs or neurodivergence unless you luck into going to the rare "integrated" school that doesn't carry the "special education" stigma.
Basically the three tier system doesn't exist to match different support needs, it exists to lower expectations based on what you can achieve without your support needs being met. Hauptschule simply won't teach you the full curriculum you'd get at a Realschule or Gymnasium and hopefully that's enough for you to achieve good grades. The German school system is only "egalitarian" in the sense that it doesn't boost those who can't pass the bar but instead lowers it for them until graduation and then sends them to compete with the rest on an "equal playing field" but with none of the prep.
I have the highest respect of everyone who actually goes from a Hauptschule to a university degree, this is probably the hardest way to get higher education imaginably around here.