I can answer a tiny portion of your question, and for only part of one European city: Rome. In 1929, the Lateran Concordat was signed between the Italian state and the Vatican, creating the independent nation of the Vatican City. The beginning of Article 7 states

The Italian Government undertakes to prohibit the construction within the territory surrounding the Vatican City, of any new buildings which might overlook the latter, and shall for a like purpose provide for the partial demolition of similar buildings already standing near the Porta Cavalleggeri and along the Via Aurelia and the Viale Vaticano.

So, in Rome, and only in the area surrounding the Vatican, treaty obligations restricted the construction of buildings that would be taller than the current buildings.

I know a bit about this.. Maybe I can help.

What defines a skyscraper? Wikipedia says "One common feature of skyscrapers is having a steel framework that supports curtain walls." There were plenty of Cathedrals that are tall and hundreds of years old, but they aren't considered skyscrapers. They don't have a steel framework that supports curtain walls.

Another definition of a skyscraper is a building that is much taller than other buildings that surround it. So in this case a cathedral that is quite tall would consider as a skyscraper, would it not?

Ancient Rome had buildings with upwards of 10 stories! Incredible!

Many flights of stairs were impractical for occupants of the buildings, in 1852 the elevator (a safe birth of an elevator) was designed and invented.

London builders soon found building heights limited due to a complaint from Queen Victoria, rules that continued to exist with few exceptions until the 1950s.

I really believe this is the answer, enough of the un-important history of buildings and things of that nature! Although the first iron-frame building with glass windows was a 5-storey building in London!

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Editing this not even a minute after posting: There was the odd exception here and there! Like This one!