Those are hugely cherrypicked examples. For example, after being wrecked at Jena-Auerstedt, the likes of Scharnhorst and Gneisenau substantially reformed the Prussian military system, to the point that come 1814, despite losing a third of its territory under the Peace of Tilsit, it could get the highest percentage of population under arms (11%. For perspective, most nations struggle to maintain more than 1% of their populations in uniform for any given period) of any European combatant. That General Staff and conscription system survived and was improved upon by Moltke the Elder and Roon, leading to the shattering defeats of Austria in 1866 and France in 1871, when most international observers bet on Prussia's opponents.

Now, whether Prussia does deserve the reputation as the most successful military power in Europe is of course highly subjective. France has been around for much longer and is much larger than Prussia ever was, and you could argue that it should have that reputation. But for its size, Prussia certainly deserves that reputation.

I think you are looking at the wrong timeframe here. Prussia's rise as a military power is normally said to have started in 1862 with the appointment of Bismarck. By 1871 they had defeated the traditional powers of Denmark, Austria, and France and more or less established modern Germany. Prussia for most of its history was weak, bit it rose quickly and led to the power that Germany had in WW1, which is why attention is paid to it.