Currently, large companies get a better rate on health care premiums - one of the few instances where price discrimination is legal in the country. The ending of that price discrimination would help individuals get coverage for a lower cost. Hospitals also discriminate on pricing against people paying cash. Insurance plans pay a fraction of the amounts quoted. A federal mandate covering that would help individuals pay their own way.
No mandate necessary - remember Obamacare made private / physician-owned hospitals illegal to be built, and ones that already existed it is illegal for them to expand. These were in the works to start going up in droves - which would have created a huge alternate marketplace for cash-driven health care (in which the actual costs of procedures are also published) that would have competed with the corporate / insurance monopolistic structures (and in turn, increased overall healthcare resources). Obamacare was designed to protect, expand, and codify corporate monopolies against this kind of competition.