The Rambam writes at the end of Hilchos Chanukah (4:12) that the mitzvah of lighting candles on Chanukah is very chaviv and a person must be careful with this mitzvah in order to publicize the miracle and increase praise to Hashem, and to thank Him for the miracles that he has performed for us. The Rambam adds that one must light candles even if he cannot afford it; if he depends on tzedakah for his livelihood he must either sell his shirt or borrow in order to attain candles for Chanukah. It is evident from this halacha that one must spend more than a fifth of his wealth on the mitzvah of lighting candles on Chanukah.
The Maggid Mishnah says that the source for the halacha that one must either sell his shirt or borrow in order to attain candles for Chanukah is from the Mishna that says that one must attain wine for the four cups of wine on Pesach at all costs, even if he is supported by tzedakah. The Maggid Mishnah explains that this is because the purpose of the mitzvah of the four cups of wine is persumei nisa. Therefore, says the Maggid Mishnah, certainly one is obligated to attain candles for Chanukah even if he cannot afford it, as is evident from the halacha that one should acquire neiros for Chanukah instead of buying wine for Kiddush on Shabbos if he can only afford one of the two.
The Lechem Mishnah there asks on the Maggid Mishnah: how can we learn that one should be obligated to spend more than a fifth of his wealth from the halacha of the four cups of wine. One is not more evident than the other; they seem identical. Why does the Maggid Mishnah state that neiros Chanukah is more obvious than daled kosos and can thus be derived from it?
When the Rambam brings down the halacha that one must light Chanukah candles lower than 20 amos, he adds that if one lights them higher than 20 amos, “Lo assah v’lo klum” – it is meaningless because the candles are not recognizable. The mefarshim are bothered as to why the Rambam added these words to this halacha.
Mori v’rabi, Rav Shmuel Berenbaum, zt”l, said that it is clear from the Rambam that the essence of neiros Chanukah is persumei nisa. It is for this reason that the Rambam adds that if one lights his candles higher than 20 amos and there is no persumei nisa, the candles are completely worthless. It is for this reason that the Rambam writes the story of Chanukah in yad hachazaka. Since the essence of the mitzvah is persumei nisa, the Rambam included the story of the neis in the halachos of the mitzvah.
As is evident from the Rambam, when one lights Chanukah candles higher than 20 amos it is not considered a ner Chanukah at all. It is not simply that one cannot fulfill his obligation with such a candle; rather the ner is not a mitzvah at all.
Now we can understand why the Maggid Mishnah writes that neiros Chanukah is more obvious than daled kosos and can thus be derived from it. Daled kosos has an aspect of persumei nisa, but it is not the essence (cheftza) of the mitzvah. On the other hand, the essence of the mitzvah of neiros Chanukah is persumei nisa. Therefore, if one must attain daled kosos at all costs, surely he must attain neiros Chanukah at all costs as well.