NASA likes to do things gradually, building knowledge as it goes along. Each step provides information used in building the next probe.
The evolution goes something like this:
- Flyby. Initial reconnaissance of a planet. Gather information on e.g. the local radiation environment, and other potential obstacles for an orbiter mission.
- Orbiter. Detailed surface mapping to help plan a lander mission.
- Lander. More details on surface composition to help plan a rover mission.
Each step costs more than the previous one. So only the most interesting targets have rovers sent to them.
There are other factors. Sending an orbiter to Pluto wasn't possible in the timeframe of the New Horizons launch: an orbiter would need a much heavier rocket than was available at the time. NH was hurried to launch because scientists had discovered Pluto has an atmosphere at the moment, and predictions were this atmosphere would collapse somewhere between 2014 and 2020, the probe had to arrive before this happened.
Because Pluto's so small and doesn't have a dense atmosphere, all braking must be done using rocket fuel. So either:
you launch at a low speed to reduce the delta-V for getting into Pluto orbit. This means the orbiter takes very long to get there (wild guess: at least 30 years instead of 9). Keeping a science team together for that long is difficult.
or you launch a probe with a huge fuel tank and engine, and you need two SLS or Saturn V to get that off the ground. This means 20 times the launch cost of New Horizons.
New Horizons goes through the Pluto system at a relative velocity of 11 km/s.
This Slashdot post contains an interesting calculation of launch weight for an orbiter:
The Space Shuttle Main Engines, one of our most efficient rocket engines, has an Isp of 4.436 km/s. By the rocket equation [this means that, to change velocity by 11 km/s using this engine, a spacecraft would need a ratio of wet mass to dry mass of exp(11/4.436) = 11.9. In other words, to stop the New Horizons probe at Pluto, we'd need to have sent along an extra 10.9 times its mass in fuel. And that's ignoring the mass of the engine and tankage, which makes things worse.
Fuel boil-off... is an additional problem: it means we couldn't use the liquid-hydrogen/liquid-oxygen propellant used by the SSMEs, but some more stable (and less efficient) propellant, which further increase the required fuel mass.
...New Horizons was launched on an Atlas V 551, which has a capacity of 19t to LEO. To send the probe plus 10.9 times its mass in fuel would therefore take an equivalent capacity of ~11.9*19 = 226t to LEO. The Saturn V, the most powerful launcher ever made, had a capacity of 118t to LEO. So you'd need two Saturn V launches, rendesvousing in orbit, to get a spacecraft with enough fuel to fly to Pluto and stop there. (Probably 3-4 launches, when you consider the other problems described above.)
The Pioneer and Voyager missions had similar constraints. No knowledge at all of space beyond Mars' orbit, budget limits because of the Apollo project.
Your initial premise is also off. We've had some high-profile flyby missions, but much more money has been spent on orbiters (Cassini, various Mars orbiters, Rosetta), landers (Viking) and rovers (Curiosity is several times more expensive than New Horizons).
Voyager and New Horizons are just the tip of the iceberg. 47 orbiters and landers, 43 flyby missions, with some overlap in that list (Rosetta is counted as both a flyby and an orbiter, for instance).