I'm nowhere near being a linguist, but it's an area of interest, and I'm trying to get something cleared up.
I know that Dutch comes from Old Dutch, or Old Low Franconian, which was spoken by the Franks, or at least a small percentage of them. I know that Old High German wasn't a unified language per se during the same time period, but a group of regional dialects that could be very different from one another, yet not so different as to be considered separate languages, like Old Low Franconian or Old Low German. I also know that over time, there was some effort to unify the German dialects of Alemannic, Bavarian, Thuringian, etc., indicating that the earlier tribes that had historically inhabited the regions where the dialects were spoken could not always so easily understand one another.
Given the above, why were Alemannic, Bavarian, Thuringian, etc. German eventually mostly unified into one language (even if some of them are still considered dialects to this day), but not Old Low Franconian, or for that matter, Old Low German? Why did the southern Germanic tribes that were conquered or assimilated by the Franks mostly speak a 'dialect' of the early German language, while the Saxons and northern Franks spoke their own separate 'languages'?
In the case of Saxony, I kind of get it, because I've often read about Charlemagne's brutal campaigns against them, and how hard it could be at times to subdue them as a people. But in that case, if the language distribution were to fall across political lines, wouldn't it be a matter of Old Dutch versus Old High German, with the Saxons also speaking Old High German as the centuries went by, or perhaps Old Dutch versus five or six other Germanic languages?
Were the Frankish nobility intentionally distancing themselves from the rest of the populace in a way that affected the development of these three languages, and Dutch and High German in particular?
Part of the issue here is your applying labels anachronistically. Those labels are also blurry because dialects and languages are very political categories.
At one point, all of these languages and dialects came from the exact same language. That language, diverged over time and became many dialects. Most basically, you had the German cluster of the highlands and the lowlands, i.e. high German and low German. These terms don’t infer class. These at first formed a dialect continuum over which gradual changes could be seen to occur.
Saxon and Franconian are both low German dialects. When the Saxons were subdued they didn’t start speaking in a high German dialect.
We call Dutch Dutch in English because they became important enough politically to distinguish. We used to say low Dutch and High Dutch. They call their language Nederlands, meaning the low land language.
The reason for this political importance was that the Netherlands became a separate political entity in the 16th century. They ceased to be another German state in the Holy Roman Empire.
Around the same time, Martin Luther wrote his Bible. He had a good understanding of several dialects and wrote his Bible to be understood by all. He based this written language on middle German dialects to increase the readability. This something like the birth of Standard German which colloquially is called Hochdeutsch. The reason that Standard German is called hochdeutsch is to separate it from plattdeutsch/ low German.
Over time, people started speaking this written language, especially people that read a lot or travelled a lot. This is why educated urbanites often speak a more standardised German than working class in the city but especially the countryside.
While extremely strong dialect crosses the dialect/language border for many (Swiss German!) the rise of nationalism in the 18th century, provided incentive to standardise both Dutch and German, further separating them.
So no, the reason that Dutch is Dutch and German is German has nothing to do with class, but rather to do with much larger political changes in the 16th century.
If class did play an element, French was the language of a lot of the aristocracy. In fact, the mother of Maria Antoinette, Maria Theresa was the empress of Austria and native of Vienna and couldn’t really speak German. Schönbrunnerdeutsch is a very French heavy dialect of German that still to an extent exists in an area of Vienna.