Admiral Matt. This is just totally irrealistic.
Unrealistic. No offense, but at first glance it seems like some of your objections are due to a language barrier obscuring my meaning. I'll try to clarify.
First of all, Frederick Barbarossa was born between 1122 and 1125. So he would not have lived many more years after 1190, had he not drowned.
He doesn't need to. He just needs to complete the crusade and return home with more glory and fewer potential rebels than he left with. As I mentioned before, given an organized succession his extremely competent heir will spend his reign solidifying the empire and attempting to expand it, rather than trying to rebuild what was lost when his father died.
Secondly, Barbarossa had been defeated by the alliance of the lombardian cities and the pope.
I'm aware. I'd been under the impression that he'd reasserted nominal overlordship by the time of the crusades, but I grant I could easily be wrong.
It doesn't matter very much, does it? Either way, the HRE is going to be fighting Lombard League who'll hold the Pope's backing. Either way, "Germany" will eventually lose for geographic, logistic, and demographic reasons. Either way, it will continue to rule the Alps and (probably) Italy's western land border. Either way, the above means that the petty states will be practically-speaking within the HRE's sphere of influence unless they unify politically. Even such a united Italy would either end up perennially losing wars to their northern neighbor, or as the junior partner in an alliance with it.
Thirdly, the contribution of England and France to the third crusade was rawly as important as the contribution of the HRE. And Richard I the lionheart was a great military commander, so Frederick I would certainly not havez stolen all the glory of a victory in the Holy land.
Most of the HRE-crusaders went home when the man died, before they'd done anything against the Saracens.
Of course the kingdoms were more important. At any rate, the Germans would have reached Jerusalem first, so....
I already said they French and English would go do their own thing, not having The City to liberate. Not clear why you felt the need to say that Richard would get his own glory as if I disagreed.
Fourthly in 1184, when Frederick launched an attack against the french kingdom of young Philip Augustus, he was blocked and had to give it up because of the mere opposition of a few princes of Low Lorraine.
Good. Trying to get more France would be ridiculous. He already ruled something like 2/5 of the modern country. Someone needed to settle down and finish the system that could have kept what they had. If you read above carefully you'll notice I didn't suggest him conquering a thing, aside from Jerusalem.
And at last, the HRE was one thing and Germany was another thing : only a part of the HRE.
Well, duh. But actually you're a bit off. Germany wasn't really another thing, because Germany as we know it
did not actually exist. At this time it'd have been ludicrous to draw a line near the Rhine mouth and say that the Low Countries weren't German. Certainly a Germany that coalesced from the HRE would be a very different creature to OTL's ethnically-centered nation state, but it'd still be a Germany. In the long run.
I don't actually see anything you pointed out that demonstrates this is inherently unrealistic. More it seems mostly a combination of semantics and misunderstanding. If you do have some information that demonstrates why this is implausible, I'd be happy to discuss it. Best way to learn.