Living in Austria, I have to pay the total of my Austrian taxes... but the US gets first cut. So if I theoretically owe $25,000 to Austria total, but $20,000 to the US, I pay the US the $20k and Austria gets $5k.
Even though I get awesome healthcare and other social services from Austria.
This sounds deeply wrong, unless Austria has an odd arrangement with the USA. It is not like this in Japan or Australia. In many countries, taxes are automatically deducted and it would be impractical if not impossible to give the USA first cut. Also, if you get residency in a state with no income tax and form a corporation in the USA you can pay yourself below the foreign earned income exclusion and for most practical purposes owe the USA nothing. I would get a second opinion from a different tax specialist.
That's deeply strange. Presumably Austria, or the EU, have an agreement with the US that allows this to happen. On the face of it, you're saying to the Austrian government "I know I earn X of your Earth Euros, but I'm going to be sending a large chunk of that out of the country, tax-free, mkay?".
Even though I get awesome healthcare and other social services from Austria.
Basically, it's the world's shittiest deal.