A check does not an employee make
The idea to carry away from Quinn v. Harris may be that calling a person an employee of the state does not necessarily make him or her such. The common law test of employee status has always been that of supervision and control over the manner in which the work is done. Hence the confusion a few months back as to whether volunteer fireman are employees for purposes of Obamacare. While often unpaid, except for stipends for training and fringe benefits like insurance coverage for any injuries incurred, volunteer fireman are definitely subject to supervision and control over the manner in which they perform their duties,
The state doesn't supervise how in-home health care workers perform their duties. The supervision is done by the person being cared for -- or the guardian of that person. Indeed, the employee and the de facto employer are often the same person, or else a member of the immediate family. Nor does the state grant these workers retirement or insurance benefits or assume any liabilities for acts done in the course of the performance of their duties as employees. The state merely serves as a paymaster. The state's rationale for the program is quasi-welfare in nature: By using Medicaid funds to pay family members to provide care at home the state can avoid the more expensive option of caring for these people in nursing homes.
The Court acknowledged this unconventional arrangement by stating in-home health care workers are not "full fledged public employees".
The theory of a union intervening with a powerful employer on the behalf of an individual employee makes no sense in such a situation. Illinois law merely set up the legal fiction of imposing dues for collective bargaining services in a situation in which precious little was ever there to be bargained for. If the Court had not opined upon the status of "full fledged public employees" I suspect the next move would be for the SEIU to lobby Democrat pols to have welfare mothers declared state employees in order to lay claim to part of those monthly checks, too.