This is the realistic scenario, where non-W2 service industry jobs provide few if any benefits, and individual policies are expensive, complicate and often require individual underwriting. Individual underwriting can require proof of a stable income (they pay a percentage of this in benefits if you get sick), and many have exclusions that can be difficult for people to fully understand, let alone compare against their own risk factors (if they're even understood). Other factors: affordability, exclusion due to medical history.
Take a look at the "service" lines in this 2014 BLS report: http://www.bls.gov/opub/btn/volume-4/pdf/disability-insuranc.... 76 percent of the service industry jobs they surveyed provided no access to short-term or long-term disability benefits whatsoever. And this is probably optimistic, it includes lots of non-contract W-2 employees. Where employer-facilitated plans are available, most employers provide them at zero or near-zero net cost to the employee (take a look at access vs. participation).
SSDI exists, but has a five-month waiting period and (IIRC) pretty substantial past-income restrictions.
I'd love to see employers get out of the health care arena altogether, but I'm also not convinced private and/or for-profit insurance plans can completely solve the problem.