Under what law would they do so?
It was controversial in 2009 even to add the "cadillac" insurance provision. What that did was to say that companies could not deduct as "cost" more than I think $25,000 a person in healthcare costs. This would mean that for all policies greater than that - that money is not subtracted from profits and the company would pay taxes on it. The very highest plans affected were for top management, including health clubs, golf memberships etc in addition to great health insurance, but it also hit some union plans. This gave those opposed to the ACA the incentive to ignore that only a very small part of the cost was above that limit - and the change was simply that the portion above the threshold could not be deducted by the employer.
This goes to the heart of why the US - alone in the world - has insurance tied to employment. The reason is that companies could deduct all payments and not pay taxes on that money. At the same time, the money the company pays for insurance is not included in the employee's income. What this means is that the government since at least the 1960s has greatly subsidized employer paid insurance. If this were considered as income, it would be on top of the income given in wages, so for many employees - the taxes would be considerable at their top marginal rate.
In 2009, my thought was that the reason this was fought was because it could lead to single payer. In fact, it is somewhat likely if a "Medicare buy-in" were made available, not just to the ACA marketplace, but as a policy that a company could buy, you might see companies moving their employees to it.
However, just as people now on Medicare, buy private Medigap plans, which are highly regulated by the government, to add a cap on medical expenditures and to insure you against costs after Medicare pays ( The plans are identified by a letter - like "F", which is the most comprehensive and most expensive and their specs are set by the government), there is no reason to think that even if the country - probably decades from now - moved to a British national health service type program - there would not be private insurance.