The Roman way was very expensive. For most of its existence Rome had a standing army, which was disciplined and capable of those formations. But Rome was a large relatively centralized empire with a significant tax base. It could afford (well, not always but usually) to pay soldiers a salary for their twenty years or so of service. Plus, provide other coveted bonuses like Roman citizenship for Germans.

None of the countries that sprung up in Western Europe after the fall of the Western Roman Empire had those kinds of resources. And large, disciplined standing armies are expensive.

If you think of the typical "feudal" structure you had the king at the top. But he was no Roman emperor, who wielded absolute power (in theory). The lords owed homage to him. And the people within a duchy or a earldom or whatever owed homage to the lord in control. So, if the king wants to get a war going he has to have a call to arms of his lords. And then the lords have to put together their vassals.

The infantry were usually made up of farmers. These men received drilling and training but they weren't paid, professional soldiers. They had jobs to do. They didn't have time for that. And no one had the kind of money it would take to turn them into that. At least not at first (later when they might the system was entrenched).

Your infantry might be supplemented by mercenaries, who would be more trained and disciplined but weren't particularly loyal to your cause.

Beyond the cost is just the level of organization necessary to keep a large standing army. A Roman army had to be fed and supplied whether at war or at peace. Rome had great roads and bridges to help do this. Rome had all of the wheat and grain of Egypt (and elsewhere) to spread around. Rome had a post system to make messages between legions possible if reinforcements or more supplies were needed. Except for the remnants of what Rome left behind most Medieval kings didn't have that.

Don't get me wrong there were many Western medieval kings who were geniuses at logistics and managed to keep large armies supplied for years at a time. But Rome didn't need a genius at the helm to make sure logistics worked except for the instances where they were moving into non-Roman territory (Trajan was a logistics genius who conquered new lands as was Caesar). They had infrastructure.

Essentially, Roman formation took discipline and a well-trained army. That took time. And those soldiers had to be paid. Few could afford that. And those who could would still have trouble maintaining it.

Beyond that I'd note that the Roman army in the West changed a lot over its history. Their tactics and weapons became a lot more similar to the Germans in the later years. Both to help fight off the Germans and because the Germans slowly became to dominate the army of the west.