The simplified grammar of modern English, relative to other Germanic languages, is usually explained by English arising as a creole between Anglo-Saxon, Old Norse, Norman French. But the Scandinavian languages, likewise, used to have accusative and dative cases, and in some cases a separate dual number. Why did they lose the cases, that modern German still has? Unlike England they weren't successfully invaded by speakers of a foreign language. Can we identify some other process, that applied most strongly to English but affected Danish, Norwegian, and Swedish more lightly, and German not at all? Noting that the Scandinavian languages still have grammatical genders, lost in English but kept in German, so they are as it were in a middle position - English lost accusatives, datives, and genders, Scandinavians kept genders, German kept all three.
While Sweden may not have been invaded by an army, they were certainly 'invaded by speakers of a foreign language': The Hanseatic League.
The League was a commercial and defensive confederation of merchant guilds and market towns in Northwestern and Central Europe. Stockholm and Visby in Sweden were both member cities of the Hanse; and Bryggen (Bergen) in Norway, and Malmö and Falsterbo in Sweden, had “kontore” (official Hanseatic trading offices). So, basically, merchants from northern Germany got powerful, lots of them moved to Scandinavian countries, and Low German became the language of trade. Then, as more Low German speakers got into various political positions, it also became widely spoken in court.
(I vaguely remember someone mentioning legislation in the 15th(ish?) century saying that no more than 3/4 or something of a city council can be German. I can't remember specifics, but it would indicate the dominance of Low German, and should be easy enough to find information on if you're interested.)
I believe the presence of the League and its German-speaking membership also significantly impacted Danish, but I don't know enough about Denmark at the time to speak to that, so let's continue focusing on Sweden. Now we have a situation where all the cool kids are speaking Low German, and Swedish is left to its own devices. Swedish gets a ton of Low German loanwords and a bunch of new grammar, including changing the verb "to become" from "varða" to "bliva" and going wild with prefixes like an-, för- and be-. But why does this lead to them losing cases? Well, let's talk about Old English for a bit now because the reason for the loss of inflection in both languages is essentially the same.
The Low German speakers weren't *trying* to eradicate Old Swedish, just like the Old Norman speakers weren't really trying to eradicate Old English either. However, when you start using several different languages in a country, it accelerates language change and simplification, especially when one language stops being the language of power. This is usually referred to as the 'principle of least effort'.
At the end of the day, if you're an Old Norman speaker and you are learning English through interactions with people around you, you're probably going to make mistakes and not learn the intricacies of the language as well as a fully immersed person would. Similarly, if you're an Old English speaker talking to a Norman who only *kinda* understands what you're saying, you're going to simplify the way you speak. This is why English lost its genders due to the influence of Old Norman, even though Old Norman has genders itself. Similarly, Old Swedish had grammatical genders and a case system, and Low German had both those things, but the 'principle of least effort' led to the gradual erasure of much of the lexical case system over a very long period of time.
Tldr: While languages and linguistic change is a really complicated and slow process, people in general are lazy and will take the path of least resistance to be understood by their more politically powerful, foreign language speaking buddy.