FM radios are built into cars, hi-fi receivers etc. – things that people sometimes use for decades and more. Unlike for TVs, you also can't just add a set-top box to a car, for example.
That said, I don't understand what's so hard about just running both digital and analog in parallel for 20 or even 30 years. This would create an incentive to upgrade to the new, digital standard (better quality, more programming etc.) without outright cutting millions of people and their legacy devices off.
The US arguably did a better job transitioning to digital radio by using a digital system (HD radio) that seamlessly falls back to an analog AM or FM signal, and they have more constraints in terms of broadcast licensing restrictions than most other countries.
