Excellent question,and I don't have a clue why they can't. At a bare minimum the state should be able to force them to follow every health and safety law on the books.
As I recall, "Dr." Gosnell's clinic in Philadelphia was completely unsanitary and should have been shut down for that reason alone. This is from the WashPost:
... What happened at his abortion clinic?
The grand jury report is full of horrific and gruesome details about the clinic that Gosnell ran for more than three decades. Patients were neglected; providers were not certified; and cats were allowed to roam and defecate in the clinic.
"The walls appeared to be urine-splattered," the Philadelphia district attorney's office found when it inspected the clinic in August 2010, months after it had closed that February. "The procedure tables were old and one had a ripped plastic cover. Suction tubing, which was used for abortion procedures – and doubled as the only available suction source for resuscitation – was corroded." ...
"The Pennsylvania Department of Health has records as far back as the 1980s documenting Gosnell’s dangerous practices," the grand jury found. "For decades, Gosnell did not staff his facility with licensed or qualified employees. He never properly monitored women under sedation. He botched surgeries and then failed to summon emergency help when it was needed." ...
More, from 2013.
Authorities in every state must thoroughly inspect - and sanction - abortion clinics for such practices, if found.