Oddly enough, only one time did I have a turbocompressor fail on the 707, and I operated several of the early models (with JT4A engines) as well as the -320B advanced.
Turbocompressors were needed because insufficient bleed air was available from the engines at lower RPM's to keep the cabin pressurized during descent. Also, using bleeds reduced the climb performance greatly, whereas the TC's were more efficient at delivering cabin air.
In addition, engine bleeds did not supply enough air for sufficient cabin ventilation with a full (189) pax load.