For a city to develop skyscraper developments the land value in the CBD (Central Business District) needs to be high enough to make the value of building up, offset the cost of commuting in/out.
In much of Europe, Urban Sprawl began in the 19thC when land value was 'low' centred around many smaller communities and so commercial and residential districts were built before the age of the sky scraper. These 'low value areas' have since developed into the 'medium value areas' that surround most European city centres. What were once outlying villages like Ealing, Greenwich or Enfield (In London for example IIRC) have thus become incorporated into the larger 'city area'.
In the US this never happened for the most part, their never were the pre-existing smaller communities which developers could 'latch onto'. Hence all development was centred around singular communities, like New York and so land value rose significantly compared to in Europe.
The end result being that in locations where you have isolated/restricted land, late industrialising city areas we see skyscrapers forming, but elsewhere we don't.
To get Europe to 'build more skyscrapers' well, you'd need to drastically change the last 1000 years of history to completely alter the demographics of social development across all/much of the Eurasia. This is more a pre=1900 discussion than post-1900 I'm afraid.