The obvious drawback with a flyby mission compared with an orbiter is of course that an orbiter could make several flyby's. I wonder if the following ideas about mission design could help make flyby missions attractive enough to outcompete orbiters for exploration of outer Solar System objects (Uranus, Neptune, dwarf planets, asteroids)?
If a flyby probe splits up into several sub-probes with instruments, they could each fly by the object of study in different trajectories. Images could be taken from several angles and a better 3D measurment of magnetic and gravity fields would be obtained. The main probe would be the only one with Earth communication capability, a long term energy source and apropulsion system. For outer planets, each sub-probe could also pass nearby one moon each. Sub-probes would only be awake on batteries during the flyby and communicate only with the nearby main probe. With 3 sub-probes + the main probe one would have the equivalent of 4 well positioned orbits by an orbiter (near a moon, such as Cassini at Enceladus).
It seems to me that fast flyby missions have several advantages compared to the same investment in an orbiter, for distance objects. Voyager being a triumph and hopefully soon New Horizons too. On the plus side:
Earlier arrival by many years, which means that the instruments will the more sophisticated and/or cheaper, giving more science per dollar invested.
Earlier science results helps design efficient follow up science, ground based or new flyby's, to target the discoveries and new questions raised.
The time value of similar high risk business investments is not rarely 20% per year or so, several years earlier delivery of results could double the present value of the investment.
Every flyby mission would fly by Jupiter for gravity assist, and near one of its moons. Then the object of interest, for example Neptune and one of its moons (before which it would split into sub-probes). Then a KBO. It would also test the limits of the heliosphere, like Voyager. So its not exactly a mayfly.