And, I think, over time we'd see more and more of that HI cost be transferred to employee salaries. Supply and demand is often taught in classes as "If this bar shifts here the economically efficient price point shifts over to here" - the portion that ends up frequently omitted is that that shift takes time. It's why some taxes are leveraged on employers and some on employees - in the end the net result is the same, but we can end up enjoying decades of beneficial inefficiencies while the market works to respond to the shift.
Yes, if HI becomes universal healthcare in the U.S., like most developed nations, then funding will be through a variety of means, inevitably involving income tax.
That said, depending on the splits, it's much more probable that the cost to "employee salaries" will be less than their typical OOP expenses anyways.