It is understandable that hiring a contract employee's LLC is risky, the answer is in the name - Limited "Liability" Company. LLC's were designed to make it easy to get the advantages of incorporation without its full formal rigid tax and accounting structural requirements. The biggest advantage is as a liability shelter. The Real Estate Development Industry literally runs on them.
They are intentionally setup to make it legally difficult for another entity to "pierce the financial veil of the corporation". The biggest advantage of an LLC is not the one your contracted with. It's the second or third that you don't have access to.
What I mean by this is that if you are an entrepreneur and you own say 5 different businesses all LLC's and one client contracted through one of your LLC's successfully sues you, Assuming your other LLC's are not contracted with the client (under the same contract) They legally cannot pierce your other LLC's to go after additional assets. This is by design.
I have several LLC's and have used them to shelter activities between contracts for years, for this reason. Granted I am not contracting as a "contract employee" in these instances clients are hiring my company. As is how it should be.
So it is understandable that large corps would not want to hire LLC's because they are taking the risk.