There is no information or news that suggests that the iPhone 14 Pro Max is always lit up. In fact, it would not be practical for the iPhone's battery life to have the screen always on. The iPhone 14 Pro Max has an OLED display that only activates when the phone receives inputs or when the user presses the screen or the side button. It has sophisticated sensors that turn the display on and off depending on the user's interaction with the device. However, some users may have encountered an issue where their iPhone display remains on even when not in use, which can be due to a software glitch. If this is the case, it is recommended to perform a hard reset or to contact Apple support for assistance.