It would make sense to increase density around existing rail infrastructure. Barcelona has 7700 km2 of space, that's a lot. They have only 750 persons per km2 on average. Especially the outskirts of the province have really bad density. For example, Sant Joan de Vilatorrada has only 660 inhabitants per km^2 and it is only 3 km from the railway station, 80 min from the Sants station. That density is worse than Phoenix, Arizona, which has 1198/km2. So there is lots of available space.
> Note that these numbers are of the Province of Barcelona. I don't know why you'd restrain yourself to the city proper.
The article, submission and discussions are about Barcelona city, not some far off town like Sant Joan de Vilatorrada (population: ~10k). No one who lives there would say they live in Barcelona, at most they'd say Manresa as that's the closest city.
But yes, if you're willing to live in the Catalan country-side, then of course Barcelona doesn't suffer from the density for you, but it's not a solution for us who live in Barcelona city.
Barcelona city proper is in a kind of geographical bowl. Look at it on a terrain map, you can see why the city is dense. It's one of the reasons I really like Barcelona, the forced density of the geography increases the amount and quality of services (especially food!) available.
Sant Joan de Vilatorrada is nowhere near Barcelona city, it's 15 hours walk away.
It would make sense to increase density around existing rail infrastructure. Barcelona has 7700 km2 of space, that's a lot. They have only 750 persons per km2 on average. Especially the outskirts of the province have really bad density. For example, Sant Joan de Vilatorrada has only 660 inhabitants per km^2 and it is only 3 km from the railway station, 80 min from the Sants station. That density is worse than Phoenix, Arizona, which has 1198/km2. So there is lots of available space.
Note that these numbers are of the Province of Barcelona. I don't know why you'd restrain yourself to the city proper. Here is a dense map of rail: https://www.urbanrail.net/eu/es/bcn/bcn-region-map.htm