Why does one opt to go to big studios?
High profile work requires bleeding edge technology - but even a simple project can mean that you need some serious custom development. Pipeline scripts, plugins, shader code, task and production management software, asset management software and so on... The list can get very long. Producing all this stuff on your own, for a single project, well it's next to impossible.
A large studio can afford to maintain and develop all these custom pieces of code and such (or buy off-the-shelf stuff when possible) because they can amortize the costs over multiple projects with multi-million budgets.
But even a smaller shop will not be able to get access to such tools, not to mention a single person.
Then there's the volume of work. The studios and production houses and publishers and such that have high profile work to bid for, they'll have deadlines and that means your studio has to be of a certain size just to get your foot through the door. One-man-armies will never be taken seriously for such work.
As a freelancer or contractor, you may have a chance. Build some assets for a game, get contracted to do on-site comp or FX work on a larger project for a few months, and maybe even get some credit for it. But then there are the issues that others have already mentioned - lack of job security, constant need to look for new clients and gigs, and so on. Still, it's a far more realistic option than opening a very small shop...