I'm curious to know if you think the shaping of Europe that occured after Hasting was for good, or ill, or neither, or both or something else? I've no motivation to ask, other than curiosity.
When the Normans were sent packing and the Cornwellian dust-up was supressed, England was left with a society ripe for the evolution of the common law and an institution of popular representation--Parliament. Social institutions that promote popular and peaceful (relatively speaking) participation grow distinctly different from the royalty and ''Divine Right'' concepts of governing that remained and persisted on the continent until the Franco-German War of the mid-19th Century and the end of the Balance of Power philosophy of foreign affairs that resulted in WW I.
So, yes, in very few words, the introduction of, and eventual elimination of, Norman rule in England was the seminal cause of many beneficial effects on European as well as world history. I doubt that the exploration and settling of the part of North America that turned out to be the U.S. would have evolved in a popular government as it did. The post-Norman England from the 15th Century and its need for raw materials, hence the growth of its sea power, and trade developed in a way that I believe would have been starkely different but for the expulsion of the direct Norman rule but with distinctive remaining influence of Norman instituted social constructs from their time of rule; both a European flavor and a ever-evolving demand for popular government and equity in law. And this doesn't even consider the influence of the Scots and Irish (post-Cornwell).
One other note to your question about the Norman era of England: The language, social customs and political/law heritage of central Europe likely would have been different circa 9 A.D.by the political, strategic and fiscal decision of Caesar Augustus to abandon plans to colonize territory that has become first the Germanic states and now a more compact Germany. The language of Rome was not superimposed on the barbarian/Sandinavian tongues as it was on the Franks and Flemish along the North Sea littoral. The Indo-European languages prevailed and skipped in a linguistic crockpot to the English. Thus, we see today the mixture of an English language that contains Frankish culinary terms with Romanace Language, Latin origin lexicon of government and law with Saxon adjectives, nouns and verbs that cross all aspects of our language.
Norman England left a legacy of language that only partially filled out the lexicon and the rest from its later Saxon ties.
I don't mean to belabor the point but you asked a probing question.