The destruction of baghdad and the spanish reconquista are convenient excuses with very little merit. The islamic empire was already very old and in decline by the time of the mongol and spanish conquests. Also, much of eastern europe was conquered by the mongols. It hasn't stopped them from embracing science. China was conquered by the mongols, they have embraced science.
Europe ( italy mostly ) was lucky because the pope decided to "submit" to the mongols and they were rewarded handsomely with trade privileges. The italian renaissance was a direct result of immense wealth generated by trade with the mongol empire.
https://en.wikipedia.org/wiki/Cum_non_solum
Without the mongol empire, there is no trade, no transfer of knowledge and technology from the east to the west and no italian wealth and hence no italian renaissance.
Interestingly enough, without the mongol empire ( or the collapse of it ), there is no columbus, no discovery of americas, no european exploration and therefore no enlightenment.
In 1480, the russians finally ended the reign of the Golden Horde and ended europe's trade link to the east. 12 years later, an italian sailor set out to find another trade link to the east.
https://en.wikipedia.org/wiki/Great_stand_on_the_Ugra_river
We aren't taught this in school but central theme of the past 500 years has been europe trying to establish trade links with the east ( primarily china and india ) that the mongol empire had provided them from the 1200s to the 1400s.