There are several reasons, but I'll list just 1.
When charge particles are accelerated, the most common technology today is to use a "linac" structure. These consist of a series of cavities. However, these cavities are power by a high-power RF source from a Klystron. Essentially, what you have in each of the cavity is a standing wave oscillating E-field along the line of motion of the particles. So when you have a series of such cavities, and you only have one RF source for each linac structure, you then have E-field oscillating back and forth in each cavity.
So what happens here is that you need to inject the charge particle bunch at just the right phase when it enters the first cavity to get an acceleration. But you must also time it just right (by building just the right length between one cavity and the next), so that by the time it leaves the first cavity, enters a drift tube, and then enters the next cavity, the E-field phase will again start to build up in the right direction. This continues though the length of the linac. This is how most particle accelerator works.
So as you can see, if you have a continuous bunch, you will not get the same effect, because you will have bunches that will enter the linac at the wrong phase.
So why do you use oscillating RF as the source of the E-field for acceleration. Because we can get higher gradient at the right phase for smaller amount of power than using a static, continuous E-field. It is "cheaper" and less taxing on power consumption.
Zz.