Largely because the same bandwidth represents a smaller fraction of the carrier frequency.
Say you want a bandwidth of 200 kHz centered at 1 MHz (the rough center of the AM broadcast band). That's 20% of the carrier frequency. But if you want 200 kHz centered at 100 MHz (roughly the center of the FM broadcast band), that's only 0.2% of the carrier. In most things, the less you have to move something, as a fraction, the easier it is.