If Kaneki had eaten another part, I believe the damage to Hide would be much greater, possibly leading to his death. Maybe the mouth was the best option

"Hide lets Kaneki eat his face to get back his strength. While it appeared at first that Hide had died in the process, he reappeared later as Scarecrow, an ally of Kaneki and the ghoul hunters."

"Kaneki had eaten the lower part of Hide's face and that's why his voice box was also eaten. He wasn't able to speak properly but he found an alternative for his voice box and you can see that on his throat."

If Kaneki had eaten another part, I believe the damage to Hide would be much greater, possibly leading to his death. Maybe the mouth was the best option

"Hide lets Kaneki eat his face to get back his strength. While it appeared at first that Hide had died in the process, he reappeared later as Scarecrow, an ally of Kaneki and the ghoul hunters."

"Kaneki had eaten the lower part of Hide's face and that's why his voice box was also eaten. He wasn't able to speak properly but he found an alternative for his voice box and you can see that on his throat."

I get these quotes from: https://www.quora.com/What-happened-to-Hides-face-in-Tokyo-Ghoul-re-season-2