In critically ill patients with Covid-19, an initial strategy of therapeutic-dose anticoagulation with unfractionated or low-molecular-weight heparin was not associated with a greater probability of survival to hospital discharge or a greater number of days free of cardiovascular or respiratory organ support than was usual-care pharmacologic thromboprophylaxis. The probability that therapeutic-dose anticoagulation was inferior to usual-care thromboprophylaxis with respect to these outcomes was high. The study has few limitations but I think it is powerful enough to indicate that full anticoagulation in critically ill patients is not advised!
Note that there is another study published in the same issue of NEJM showing an increased probability of survival to hospital discharge with reduced use of cardiovascular or respiratory organ support in noncritically ill patients defined as the absence of critical care-level of support at enrollment).
It seems that the benefit of anticoagulation is seen only when started early in the course of the disease.