We do really need to have a serious conversation about single-family homes; you will even find them right next to metro stations. Some of these low-density neighborhoods really need to be demolished and reconstructed into higher-density housing that can still reasonably house a family.
The city centers are the most expensive, because vast majority wants to live there. Further away is less expensive and even mode further away is even more expensive.
Most if not all european city centers are no dystopia. They are perfectly compatible with having familly.
Are home prices just outside the city center stagnant?
Pick the low-hanging fruit. More housing outside the city centre (with requisite transit infrastructure) still means more-affordable housing. That, in turn, should relieve pressure on the centre.
This is obviously untrue if the prices have risen.
But in contradiction to the article, just up the road from me, practically a small town was built of high density housing in what i would still consider “the city”, but with amenities and improved public transport factored in