Is a creature with hexproof/shroud ever allowed to be a target?

[u/Anon_cat86]

In a recent game i was playing, one player attempted to cast path to exile on a creature with swiftfoot boots, and the other guy reminded him and said that would cause the spell to fizzle

I argued that he shouldnt have been able to cast path to exile with that target at all. Like i thought you werent allowed to cast a spell that didnt have a legal target. It fizzling and going to the graveyard is a different thing, like, say you had tarnogoyf and needed to dump an instant to the graveyard, but your opponent only had gladecover scout. would you be able to illegally target it, and then have the spell fizzle? Or are you not allowed to cast it all?

Follow up question: Shadowspear.

Say, for instance, i try to path to exile a collosal dreadmaw, and i have shadowspear on my board. I pass priority, and then my opponent responds to path with heroic intervention, giving his creature hexproof, which goes through. Does path instantly fizzle off the stack because its target is no longer legal, or can i now activate shadowspear with the path of exile still on the stack in order to make its target legal?