Nit'ei Gavri'el addresses this, quoting an opinion that the Ram"a may have been addressing it as well when he gave his examples of what coins people would give in various lands. The context in which he brings it up is the case of a person who does not have any coins. Despite recommending that that person use whatever form of currency they do have available (such as a bank note), anonymous mention is made of an opinion who insists on using a half denomination coin.
In defense of the position that the mitzva can be fulfilled without a half denomination, Rav Tzinner quotes Vayish'al Sha'ul with the following, apparently proactive, rationale:
נטעי גבריאל פורים פרק כו קטע ו הערה יב
ובזמנינו שנתחדשו המטבעות ואין לנו בכ״מ מטבע ששם מחצית עליה, שמעתי אומרים דכוונת הרמ״א ליתן המטבע היותר קטנה שבמדינה . . .
And in our times, as currency has modernized, and not every place has a coin called "half", I've heard they say that the Ram"a's intent was to give the country's smallest coin. . .
That author then rejects this interpretation of the Ram"a, based in part on earlier sources, and in part on the Ram"a's own words in Darkei Moshe. The conclusion is that using a half denomination really is crucial to the non-mikdash-time mitzva because it is meant to be a commemoration and the mnemonic is the very fact of it being called a "half" just like the "half shekel".
BUT THEN, he picks back up on an idea that had been raised by the Ram"a in Darkei Moshe of people who used the larger of two possible half denomination coins because its weight was closer to the equivalent weight of 10 gera that appears in the Torah. He extracts the latter from that line of reasoning to propose that if one had no half denomination the Ram"a would prefer them to still accomplish the mnemonic by some other means such as approximating the weight of 10 gera.