See also https://en.wikipedia.org/wiki/Braess's_paradox

> adding one or more roads to a road network can slow down overall traffic flow through it.

Like it or not, that increased car traffic delivers more utility.

You can't have a car free metropolis. That's a contradiction.

> Like it or not, that increased car traffic delivers more utility.

It rarely delivers enough utility to even compensate for it costs.

> You can't have a car free metropolis. That's a contradiction.

It's absolutely not, your assertion is outright nonsensical.

Car-centricity is by far the worst way to build a metropolis.

“Car free” is one of several ways to not be “car-centric”, but not the only way. I believe it’s possible to make a car-free metropolis, but I don’t know if any (modern) metropolis demonstrates this.

Sure but I’m not the one which set up this straw man dichotomy and saw no reason to care for or acknowledge it.

The utility vehicles, buses, delivery of goods to stores etc are percentage of overall vehicles on the road and require little infrastructure compared to using cars as main individual mode of transportation.

Paris is certainly trying. The idea that you need a car to move around a city is probably cultural.

Paris is hardly the only city doing that either, and far from the first.

While a fair bit smaller, Amsterdam is probably a better example here (and it helps that they got started in the 90s).

And as points of difference (aside from size), Amsterdam has a much smaller metro network, but a larger tram network (Paris completely shut down its tram system in the late 30s and has been rebuilding it since the 90s, whereas Amsterdam's tram network was never completely shut down, and while a number of Amsterdam's tram lines were switched over to buses in the 40s and early 50s, trams got repopularized very quickly, as soon as the late 50s).

You can't have a car-free metropolis, but you sure can have a metropolis where cars are used by much, much fewer people than is typical today.