How does radio bandwidth restrict the choice and use of science payload on interplanetary probes?
Sample returns are expensive and risky.  Radio is simple and reliable.  Radio bandwidth on a particular mission is determined by several engineering tradeoffs.  Higher bandwidth requires either larger antennas, more output power, or more complicated processing.  

Spacecraft are typically limited in mass, power and compute capabilities. What most missions have plenty of, is time.  Lower bitrate takes longer, but allows more mass and power to be used by other experiments.  This is often a highly desirable tradeoff.

Missions like New Horizons that have a fairly limited time to record lots of observations do so to a data storage device, and then spend months or years relaying the data back to Earth during the long coast to the next target.