I know in sports events where lots of people are standing around and watching, synthetic line has its merits, not only that if it breaks who cares there are extra's all over the place.
On the business side, regardless of strength, wire is the ultimate in durability bar none. As an example, we were putting a new antenna parts on top of a tower that required the use of synthetic winch rope instead of wire cable for safety from electrical shock. While we were at lunch ie 45 minutes that rope nearly rubbed itself in two, we had to replace it before we could continue it would have taken days for the same size of wire cable to have done the same thing.
No synthetic winch line I have used was as tough as a wire one of the same size, for some that may be a factor to consider. Visualize a hacksaw or 50 grit sand paper rubbing on each and you will see what I mean, its hard to always keep your line off rocks, snags, or sharp burs and in these kinds of situations wire rope is superior.
There are down sides to wire rope, I am not suggesting there isn't, there is no such thing as a free lunch, it weighs more, requires gloves to handle, you have to keep people out of the way, but it is far more durable and its very very very rare that wire rope breaks when used correctly.