New Horizons, like many other spacecraft, used gravity assists from planets (Jupiter in its case) but the specific combo of assists available to Voyager will not in fact occur again until the year 2224 [0].
Sure, I mean we won't get to do a Grand Tour again anytime soon but we can and did send things either to planets or heliopause and beyond.
As a nearby comment mentions, Voyager were flybys so now that it's done and even if we could ROI may very well be lower than sending more focused orbiters (for planets and moons) or deep space crafts (for peristellar/interstellar)
[0] http://www.gravityassist.com/IAF3-2/Ref.%203-143.pdf, section 3.4