The killer feature of FM synthesis is generation of inharmonic sounds. Classic analog waveforms (sawtooth/square/triangle/sine) are all perfectly harmonic, i.e. the frequencies of the higher harmonics are at integer multiples of the fundamental. Subtractive synthesis shapes the amplitudes of these harmonics but doesn't add any new ones.
Subtractive synthesis is still musically useful, because most musical instruments are harmonic or almost harmonic, but tuned percussion is a notable exception. It's very difficult to get a good bell sound out of subtractive synthesis. FM can produce inharmonic sounds, where the higher harmonics are at non-integer multiples of the fundamental. It's much easier to get good bell/chime sounds out of FM synthesis.
And the "almost harmonic" instruments are very popular (all plucked or hammered string instruments, with the inharmonicity more pronounced with thicker strings, so especially bass and piano). By adding a little inharmonicity, FM synthesis can produce more realistic versions of these sounds than subtractive synthesis.
Additive synthesis can also produce inharmonic sounds, but this requires an oscillator for each harmonic, so back when FM synthesis first hit the market this was unreasonably expensive.