Again, the same reason they ditched Belgium. I don't know how many times I need to repeat myself on this point. The Rhine being inhabited by Germans is irrelevant.
They ditched Belgium for compensation, not just because they didn't like that part of Europe. They were always trying to ditch Belgium for compensation. They tried to ditch Belgium roughly 40 years earlier through a trade with the Bavarians but didn't actually follow through because they weren't able to close the deal and get anything in return. Earlier than that, they promised it to France in the 7 Years War for help recovering Silesia. No Silesia, no transfer of Belgium.
Even at Campo Formio, after Austria had been stomped, they formally traded it for Venice. That's essentially the situation restored in 1815. They never found Belgium to be worthless, just strategically undesirable.
So if Austria is offered Cologne and Trier, without being asked to surrender Galicia or any other territories in return, there's no reason they won't accept.
Francis was already talking about war (whether or not he was serious is up for debate) if Bavaria did not yield on Salzburg. Of course, in retrospect, Bavaria got the better end of the bargain.
It seems as if Francis and Metternich were talking about a lot of wars. One wonders if their support among Bavaria and the other German states vs. Prussia and Austria would have been as solid as you suggested earlier.
Napoleon's return will not wipe away the British public opinion that any annexation of Saxony by Jan 1815 was illegal. And if the Tories want to remain in power, it's in their best interest to maintain such a stance. Plus, Wellington is not a part of the appeasement faction.
Britain is not going to prioritize Saxony over forming a coalition to remove their great enemy in France. Nor are Russia and Prussia going to rush to war with France while their erstwhile allies are still arming against them for the aftermath. By far the most likely turn of events is a compromise where everyone gets something of what they wanted before Napoleon reappeared, not one in which everyone just gives Metternich everything he wants because he's so good at being stubborn. The second most likely outcome is failure to form a coalition at all, and then Napoleon gets to stay in power. At that point everything is up in the air, far more than Saxony.
It's not about compensation, it's about abandoning all your prestige. Austria by January 1815 was not going to throw away its influence in the German states to appease Prussia. Because recognizing the unilateral annexation is as good as geopolitical suicide for German hegemony.
Let's not be so dramatic. Austria accepted many unfavorable treaties between 1797 and 1809. States were created and destroyed. It's realism and it enabled Austria to continue as a going concern. Historians tend to look back on the era after 1815 as something completely different to that before, but at the time it would have been just one more treaty, one more turn in the game. Maybe the following period wouldn't be as stable as OTL without the willingness Russia and Prussia showed to back down in 1814 but that doesn't make an alternative outcome unthinkable.
Austria would rather the entire Congress end and no treaty come about than yield in this regard. It's either Prussia getting Saxony or the Tsar getting Poland, but not both, and it needs to be earlier than the turn of the year.
Austria may want this and on its timescale, but I already explained that nobody was actually about to declare war and march to liberate Saxony, much less Poland, at the end of 1814. I suppose the host has the prerogative to close the session, but I don't think many other participants would react well to that. Nobody actually wanted to go to war again. If the Congress ends, then the next Congress happens somewhere else after the Hundred Days, with or without a surviving Napoleon participating, and the issues are settled there.
But considering any extreme heighten on war, this can easily butterfly Napoleon's escape from Elba.
Anything can butterfly anything, but chances are a more public Allied disunity is only going to encourage Napoleon to return to France and embolden his supporters there.