Arrow calls scissors an "irrelevant alternative" to the race between paper and rock (since scissors doesn't win but makes paper lose). This is just unreasonable -- if there exists a rock-paper-scissors loop among the top preferences of voters, then the voting system should at least acknowledge that reality and make sure it picks someone within that loop (the particular winner is somewhat arbitrary).
And, indeed, if you instead use a more reasonable criteria that requires just that -- that the winner must come from the smith set -- then all of the "reasonable" criteria are satisfiable. Hence the overhyping of Arrow's theorem.
You are right, though, that basing analysis of voting systems on rigid criteria can lead you into trouble. Over-reliance on Arrow's theorem is just an example of that.
IIA is an extremely reasonable quality of an individual's preferences. Although you could probably construct pathological cases where it might sort of make sense for an individual to swap his preference of X and Y when Z is introduced, I contend that it would be exceedingly rare. Showing that IIA is impossible to guarantee (at the same time as other criteria) in an aggregate of preferences is a pretty big deal.
Arrow's theorem does not say or logically imply that, if there is a cyclical Smith set, the voting system shouldn't acknowledge that and pick someone within that loop.
For example, you confidently dismiss plurality voting, but you can't really do that unless you establish what the goals of your voting system are. These goals need to be clearly defined, you can't just say your goal is "making sure everyone has a voice" or "making sure the best candidate wins." That's really all Arrow's theorem says: there are several criteria that most of us agree are desirable, but you cannot have all of them.