People become freelancers/contractors because it typically pays better than full time gigs as well as allows the individual to pick what they work on.
There are many reasons why organizations use freelancers/contractors but at the last place I was at it was because they are easier to fire than a full time employee. The organizations also don't have to pay for benefits for that contractor/freelancer so that saves them money as well.
Depends on the industry and location and what you consider freelance/contractor. There a bunch of contractor jobs in Chicago but they are in fact W2 (full time employees) you just work for the firm doing the contracting. Corp to corp exists but I'm not privy to the details so I can't answer you there.
There are many reasons why organizations use freelancers/contractors but at the last place I was at it was because they are easier to fire than a full time employee. The organizations also don't have to pay for benefits for that contractor/freelancer so that saves them money as well.