I think I read somewhere that all anthropoids have an innate fear of spiders. Even chimpanzees, gorillas etc in zoos go 'apeshit' (sorry, couldn't resist that pun, hee hee!) if shown a plastic, or a real spider. So I conclude that fear of heights, claustrophobia and so on are there to keep us safe. Maybe in early times, many spiders were actually venomous and it behoved us to fear them and run away.
Fear is quite a useful state. I'm afraid to walk alone down a street in the dark. (Nowadays, one could be attacked).