While the planetary alignment was convenient, it isn't exactly necessary on RTG-powered spacecraft. Pioneer 11
visited Jupiter, then flew to almost the opposite side of the solar system to visit Saturn. Longer travel time (and greater chance of equipment failure during that time) is the only drawback.
Another factor working against a Pluto encounter was the lack of sunlight that far out. During Voyager 2's encounter with Neptune (which was slightly further away from the sun than Pluto at the time), sunlight was so dim that NASA had to reprogram the cameras to take longer exposures than they were originally designed. Then someone calculated that Voyager 2 would be moving so fast that the photos of Neptune would be blurred just by the changing parallax between the spacecraft and Neptune. So they programmed the spacecraft and cameras to rotate slightly during the exposures, effectively panning the camera to cancel out the changing parallax.
All this happened so quickly they got just one shot at it, and they had to do it blind. By the time the first near photos reached Earth, if they had turned out to be blurred, any correcting instructions sent to Voyager 2 would have arrived after the spacecraft had passed Neptune. So NASA wasn't even sure if the closest Neptune and Triton photos would even be aimed correctly. Heck, they weren't even sure they were going to make it to Triton (Voyager 2 flew less than 5000 km over Neptune's North pole to get to Triton). But as it was the last major destination and they'd recently discovered an atmosphere on Triton, they figured what the heck and rolled the dice. As it turned out, they got everything right, and Voyager returned some spectacular Neptune and Triton photos.
A Pluto encounter would've run into the same problem. Except Pluto is a much smaller target than Neptune, whose mass (and therefore gravity) is much less accurately known so properly aiming the camera is even trickier. Even New Horizons (with newer, more sensitive cameras) is going to have to use the same panning trick Voyager 2 used at Neptune. New Horizons is moving fast enough it could cover the distance from the Earth to the Moon in less than 8 hours, so all the close-up photos and measurements of Pluto are going to be over in a matter of hours. And it's basically guiding itself - providing the most accurate measurements we have of Pluto's mass so we can fine-tune its trajectory as it approaches Pluto.