There are some, but you wouldn't be able to buy shares in the better classes of mutual funds, like Vanguard InstlPlus. Those rely on the whole company buying the same shares to meet the minimum investment requirements.

i've worked for a company with a plan that offered something like this, however there was an additional fee on top of whatever the costs were. And like the sibling comment says, you get the public etfs, which wont get any bulk savings(oh how i miss my 0.02% ER institutional shares). You are unfortunately still stuck going through the company the employer chose. Very rarely you can get a plan that allows you to roll over while still employed, so if you did that say, annually, you could self direct then.

employer matching was separate, you and the employer add money, then you choose what to do.

IMHO, 401k should go away and the deductible limits on IRA should be raised to compensate and let people do their own thing.

Yeah, some plans offer self-directed brokerage options, with an administrative fee on top of things. Otherwise, with, say, Employee Fiduciary (one of the dirt cheapest Vanguard-backed administrators out there), we chose 40 funds to offer our employees, though almost everyone has just stuck with the Vanguard Target Date options.