The alumina cannot be replaced with plastic for 2 reasons.
It must be hermetic, to keep the argon inside and the air outside, for the lifetime of the bulb.
It contributes to the high efficiency, by reflecting both the visible and the infrared light and preventing thus the heat loss from the lamp.
Nonetheless, alumina is less fragile than ordinary glass.
It might be possible to replace the quartz window with some kind of glass window, for a lower cost, but not with any kind of plastic, because it must also be hermetic and it must be usable as a substrate for thin film deposition in vacuum and it should have a coefficient of thermal expansion matched to those of the multiple layers of the infrared-reflecting filter.
It must be hermetic, to keep the argon inside and the air outside, for the lifetime of the bulb.
It contributes to the high efficiency, by reflecting both the visible and the infrared light and preventing thus the heat loss from the lamp.
Nonetheless, alumina is less fragile than ordinary glass.
It might be possible to replace the quartz window with some kind of glass window, for a lower cost, but not with any kind of plastic, because it must also be hermetic and it must be usable as a substrate for thin film deposition in vacuum and it should have a coefficient of thermal expansion matched to those of the multiple layers of the infrared-reflecting filter.