There’s not a lot of synergy between processing WiFi or 3G/4G/5G and processing radio (whether AM, FM or DAB), nor are the frequencies particularly similar.
Nevertheless you and @amarok may well be right about some of the motivations.
Another potential motivation is that a broadcaster that is serious about internet radio may want to pay for at least a CDN if not internet broadcast points (really multicast) within the core internet. So that’s another revenue opportunity for the mobile network operator (the other side of the coin compared with the customer paying for more data).
Yes, I think I have an early mobile phone packed away somewhere (somewhat older than yours) that had FM radio transmission (very short range of course, for the intended usage - the sort of thing that would be done with Bluetooth today). Phones used to have FM capabilities.