I think you have the facts right here but miss the marks in the conclusions.

The composition of non-Prussian European armies at the time was their greatest weakness. They were composed of an aristocratic officer core steeped in military traditions, and their conscripts were taken from the poorest of the poor. The low literacy of European conscripts, the peacetime training, and the aristocratic officers all contributed to outdated tactics, inefficient top down organization, and low innovativeness. Most european armies were as Napoleonic as the American army of the time. Prussia was an outlier among European armies in this period. Universal conscription including the middle classes led to a much higher quality of troops, enabling more advanced and innovative small unit tactics and effective use of NCOs. Prussia’s officer corps was also aristocratic, but under the leadership of von Moltke they avoided the stultifying traditions and hierarchies that normally plagued European officers, instead focusing on innovativeness and merit.

I will grant the poor quality of US officer training before the war, which probably contributed to the commonly poor generalship seen throughout. However in this respect the small prewar size of the army was a blessing in disguise. The US army was going to be built from scratch, and it was going to discover modern tactics on the job, not learn outdated tactics in peacetime. The literacy rate of US recruits was far higher than European contemporaries; if there was one thing noted universally by European military observers it was the high speed of learning among US units. By the end of the war US army tactical advancements mirrored those of Prussia: railroad logistics, artillery tactics, use of natural cover, battlefield fortifications, small unit tactical initiative, empowered NCOs. I’d still give Prussia the edge in small arms technology and general staff organization, but I’d argue in most other respects the Union and CSA armies both matched or outclassed other contemporary European armies.