Not sure about European cities or if they directly compare to US. Most major metropolitan areas in the Midwest and East coast region are seeing people leave for suburbs or even small town America.
It's because suburbs are subsidized in the current system. Roads, infrastructure, and other upkeep costs are paid by the entire city but since the denser regions are more productive/profitable, they end up paying for the services that suburban residents are using. If suburban residents had to pay for the real cost of their housing, then I think it would be a lot less appealing. Building suburbs is terrible city planning and it's sad that cities are continuing to endorse them.
Do you have a source for this? Denser European cities seem to have much higher happiness than people living in single family residential suburbs.