But most places(at least around the EU) have already announced that the vaccine will be free - so there is no question about affordability?

The taxes still paid for it twice

In what way? Yes, the taxes paid for research, then taxes paid to purchase the product. But if everything was state owned top to bottom, the taxes would have had to fund research, then manufacturing, production and distribution. I wager the amount of money spent would have been exactly the same, so it's more like an accounting trick than an actual difference.

Its not about manufacturing costs. The companies continue to own the patents and after some period of time have every plan to start charging for use of it. This means they can get rich for decades off of the taxpayer-funded research. Meanwhile the governments have agreed to take on the risk by buying tens of millions of doses before they vaccines are even approved which means some of them will likely be waste due to either not getting approval or coming after more effective drugs.

Socialized risk and privatized profits. A capitalist's dream.

To go back to your highway analogy, its as if the government contracted for the entire interstate highway system to be built and then let various private companies charge a perpetual toll to use the roads in addition to the money they made for building it.

Its not an accounting trick, its a perpetual royalty on the taxpayer's expense if the drug works (and a profit even if their drug never passes Phase 3 clinical trials).