Why don't dogs usually develop sore throats, or lose their voices, after barking for a long time?

Dogs evolved to bark so their vocal arrangement is not the same ashumans. Barking does not require the same exercise of the vocalcords as yelling does in humans thus they can bark almostendlessly.

Because they do not possess the same vocal cords arrangement as Humans.

Barking cause lower amount of muscle strain in Vocal cords compared to when humans are yelling.

This make dogs able to barks endlessly without having to create any damage on their vocal cords.