Invest that on the side and you'll have built a fortune within a decade and a half, while your German friend has nothing significant in savings and is still living hand to mouth.
And we haven't even mentioned the differences in career steepness: After a few years it's not 80k vs 160k anymore, but more like 90-100k vs 200k+.
Also if you compare the best places in each country than you are looking at something like 100k vs 300-400k.
Again, I have been trying really hard to see if all the benefits you mention really offset this monetary discrepancy, but it's just too huge.
The 4k extra take home is more significant if you move to a LCOL place once you have acquired your fortune, not if you stay in the States. I would argue things like FIRE or Lean-FIRE are only slightly easier to achieve in the US than in Germany because of the comparably HCOL.