It’s not practical. Patients on ECMO require anticoagulation, as do patients on cardiopulmonary bypass. This is a problem common to all systems which expose blood to foreign surfaces and pass it through pumps. Your hypothetical anticoagulated soldier with such a pump would bleed out lickety-split were they to suffer as much as a minor cut.

Also, such a system would likely require giant cannulae placed in rather inconvenient places, e.g., the neck, thigh, or chest, as in ECMO. That would limit movement significantly.