Most of those phones are designed where that LED is more than just a flash. A flashlight on a phone is a critical feature allowing safety in dark areas, finding of objects like keys dropped or the lock on a door at night, signaling if lost of on the side of the road broken down trying to attract a police officer, etc. It does not take much power to run that led compared to the bright led's used to backlight the screen, the screen usually(but not on the newest led technology phones) uses more power than just that led next to the camera being on when the screen is is on its brightest setting, and barely generates much heat compared to the cpu chip. Finally, the led isn't necessarily near the processor, memory, battery, or other heat producing modules to assist with things like this, so I doubt this is really ever an issue unless you know of a specific case you've experienced.
In short, the phones are generally designed structurally to allow for the continuous operation of that led 'camera flash', it isn't actually that power hungry. Your only issue is shortening the battery life significantly, which browsing on the internet does as well and similarly in my experience.