By this time I would have thought a lot of the more advanced European powers would have the money and technology to create a Roman-style infantry army. I'm aware of things like the rodeleros, but why did armies choose to fight with massed pikes instead? Hadn't the Roman legions proved to be more flexible than the Macedonian phalanx?
In the most significant sense, late medieval/early modern armies did resurrect the Roman way of fighting: larger, more centralized states developed administrative and financial apparatuses that were able to raise and maintain large bodies of soldiers in the field for sustained campaigns. The capability to put large numbers of troops in the field matters more to military success than copying the exact tactics of a bygone era. Replicating the sword-and-javelin armament of Roman infantry wouldn't be nearly as effective for late medieval armies, when plate armor (that wouldn't be affected at all by javelins) was becoming more and more affordable for the average soldier. Even the cheap munitions plate available to the average Hapsburg pikemen in 1530 would be much more protective than the linothorax of his Macedonian counterpart. Pike formations were supplemented by other, shorter weapons: the proportion of halberd to pikes was often a fixed ratio that varied from country to country. The inflexibility of pikemen was a known weakness that was often exploited, but ultimately massed piked proved themselves capable enough they were only eventually supplanted by increasingly sophisticated handheld firearms.
In addition to what MI13 mentioned in their excellent answer, you have to keep in mind the tactical employment of Early Modern pike formations bore only superficial resemblance to Macedonian phalanxes. They both carried pikes, and that was it. The Spanish, on the cutting edge of military development in the 16th century, fought in the tercio; in a bastioned square, with muskets in every direction, they usually stood their ground even when completely surrounded, whereas Macedonian phalanxes often collapsed when outflanked.
In another sense, Early Modern armies like Maurice of Nassau did emulate the Roman way of war; they compensated for the limitations of muskets by countermarching, rotating men in a file to keep the men ready to fight in the front rank. They built sophisticated logistical networks. Their greatest strength was the scientific application of engineering to construct and overcome fortifications. Is there anything more Roman than that?