Up until this point there had been no close-up pictures of the outer solar system. The planets were in positions so that the probes could effectively "steal" some of the planets momentum to increase their speed. This is done very often and is called a gravity assist, (I'm on my mobile so I can't link it but look up Rosetta's trajectory if you want to see gravity assists in action.) but the opportunity to send a probe so that it can get gravity assists off of several of the outer planets in quick succession only comes around about once every 175 years. Which is why the two probes were launched in right after each other.

It's important to keep in mind that the Voyager program wasn't in any way a "sudden" decision - planning stages reached back to 1960s and the idea of a "Planetary Grand Tour." The launch of the Voyager program in 1977 came on the heels of the Mariner (Venus and Mars) and Pioneer (Jupiter and Saturn) programs; in addition to the Viking landers on Mars. Also, the alignment of the outer planets (Jupiter, Saturn, Uranus, and Neptune) allowed for a single craft to use gravity assists to visit each one, instead of burning fuel for course corrections or launching four separate missions.

Although both could have seen all 4 planets, Voyager 1 was routed to make a close approach of Titan (Saturn’s moon), after which her trajectory took her outside of the orbital plane. In the full historical context, Voyager is very much a child of the space race. While it was launched in 1997, this Grand Tour idea had been under consideration for over a decade.

One of the biggest motivations was at the time how little we knew about the outer planets. The original mission wasn’t just to send a craft into deep space, but to explore the Gas Giants in depth. The Interstellar Mission only began after the probes had completed their primary fly-bys of the planets. Prior to Voyager, there had only been 2 missions to Jupiter and 1 to Saturn. In fact, Voyager 2 remains the only spacecraft to visit Uranus and Neptune. A few top-level discoveries of the Voyager program include the first extraterrestrial volcanic activity (on Io), the rings of Neptune, 10 moons of Uranus, and evidence for a liquid ocean underneath Europa.

As for why we haven’t done it since, I would argue that the discoveries from Voyager allowed space agencies to decide what the best targets would be for scientific discovery. Think of the Voyager probes as a scout mission; and that they paved the way for missions to Jupiter (Galileo) and Saturn (Cassini-Huygens) that made important contributions to astronomy and the understanding of how the solar system was formed.