Well you could I suppose, but it is not so simple as finding a transformer with the proper input/output voltages. So good luck. The cap, of course is for power factor correction, but when the lamp strikes, there is virtually no resistance to current flow, so the ballast (transformer) regulates the current to keep the lamp from burning up. They provide very specific operating characteristics for the lamp, as outlined by the lamp manufacturer's specifications, and in accordance with ANSI specification C82.4.
With high lamp current European spec lamps, especially the most popular these days in this hobby, there is no ANSI specification, which further complicates the issue. So not only are "we" at the mercy of transformer manufacturers, but also the lamp manufacturers who are targeting the "niche" hobbies of hydroponics, and aquaria. (higher color temp lamps.)
The writing has been on the wall with MH lighting for quite some time now, as the legislation has already started. T5 is solid, and time tested, though the lighting suppliers are doing their best to complicate it; LED is in its childhood (not really time tested yet,) plasma is out there.......... not there yet....
Jim