Our Gemara Right at the beginning of Amud Aleph tells us that though it usually is preferable to recite the Hallel on a “Satisfied soul and full stomach“, a different rule was made for the people of Mehoza. Ordinarily, if there is a public fast due to a drought and the rains fall before midday, the fast is suspended, people go home to eat and celebrate, and then go back and say the Hallel Thanksgiving prayer. But since the people of Mehoza tend to drink and become inebriated, the rabbis made a special rule that they should say the Hallel Thanksgiving prayer first. (In general, Mehoza is known in the Talmud To be a cosmopolitan metropolitan area, see for example Gittin 6a. So I suppose they worked hard and played hard.)
In a certain sense, the Gemara is capturing the tension of two poles in observance, rejoicing and celebrating God in joy, and the concern that too much revelry would lead to a lack of dedication and fear of God. The Gemara could have played it safe, so to speak, and had everybody recite the Hallel prayer before they eat. But that’s not really the answer, because it was supposed to be recited in a joyous state. Yet, the rabbis were pragmatic and realized that the people of Mehoza would not have the patience nor the dedication to properly celebrate first without becoming drunk and then come back to Shul and pray.
It makes me wonder about the Maariv and Kiddush Levana we recite immediately after Yom Kippur. On the one hand, this is a great opportunity to offer up a completely selfless prayer, still on an empty stomach, showing God that we are ready to serve him. On the other hand, the hunger and the need to rush frustrate and ruin the proper prayer. I would say, if there is an assessment that people are unable to pray without rushing, it’s probably better to go home and eat first and appoint a Shomer to remind you to pray maariv, and afterwards conduct a proper, leisurely maariv. This Gemara though is not a proof to this point, as possibly only by Hallel were the rabbis concerned that it be recited with joy. My discussion is less halakhic and more hashkafic. (Also, one must still recite havdala before eating, and Shema for good measure, and even so when you eventually pray maariv, you still say ata chonantanu, even if you made havdala (Mishna Berura 294:1). But ultimately, if after you eat you are not going to concentrate either, you might as well be like the people of Mehoza, and pray before. On a practical level, that is probably why the custom, in the end, to just to daven maariv right after Shul Yom Kippur night, though sadly it is a challenge not to rush.
Translations Courtesy of Sefaria, except when, sometimes, I disagree with the translation 
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