The purpose of ventilation in these severe ARDS patients is to augment oxygenation of the blood, using a combination of techniques including end-expiatory positive pressure and inverse-ratio ventilation, among others, and support the fatiguing respiratory muscles. Because the lungs of COVID-19 patients are already injured by the infection, they are very prone to further ventilator-associated injury. Modern intensive care ventilators have complicated computer-controlled 'modes', which allow precise regulation of ventilatory volumes, pressures, rates, timing, and gas blending. The ARDSnet trials in the early 2000s demonstrated the importance of carefully managed 'lung protective' ventilation, poor quality ventilation is likely to cause further lung injury and make the patient worse, not better. Therefore amateur ventilators are unlikely to be beneficial in COVID-19 unless they can provide similar lung protective ventilation, which would make them quite complicated.
Additionally, ventilation is just one component of the management of sick COVID-19 patients. First you need to pass a breathing tube into their trachea, which is a challenging and risky procedure when performed by a skilled operative in a otherwise well patient, let alone someone on the brink of respiratory failure. Once intubated you will need to keep them deeply sedated, otherwise they will strain against the ventilator and make effective ventilatory care impossible. This requires equipment, drugs, and skilled staff, all of which are going to be in short supply.