The desire for ongoing health benefits is a big part of the explanation:
The [union] locals combine…welfare plans together in the centrally administered Motion Picture Industry Pension and Health Plans, while the guilds manage their own individual plans. In either case, the system that has emerged in practice has the signal advantage that individuals’ benefits packages are not tied to any single employer but are fully portable from firm to firm. In this way, the Hollywood unions and guilds play a role somewhat analogous to that played by the government-sponsored Intermittence du Spectacle in France, which provides unemployment compensation and other benefits to wokers in the French entertainment industry.
Of course Hollywood is known for its short-term and volatile employment, and for the temporary nature of its projects. The explanation for unions continues:
Additional important functions of the unions and guilds are (a) the codification and regulation of professional categories, (b) accreditation of members’ work experiences, and (c) the provision of educational, labor-training, and other qualification-enhancing services.
That is from Allen Scott’s new and excellent On Hollywood, The Place, The Industry; the book is an applied study in economic geography. Here is my previous query about Hollywood unions. And somewhere in here is a paper on whether Hollywood offers a possible model for reforming our health care system.
Addendum: Matt Yglesias adds: "the Writer’s Guild of America (of which my father is a member) plays an important role in arbitrating credit disputes. Screenwriters often get fired or otherwise leave projects in development, which are then finished by someone else. Oftentimes, three or more writers (or teams of writers) will cycle through a project before it’s completed. Someone needs to look at the final project, decide which writers deserve credit, who deserves the primary credit, and who — if anyone — should get a "story" credit. Contracting these responsibilities out to the Guild lets studios duck a series of nasty disputes in whose outcome they have no real interest. It also protects writers from directors or producers who might want to muscle their way into screenwriting credits."