You have an excellent point, and historically, yes, you did need something plugged into a headphone jack to facilitate the rx of the transmission, however, this isn't strictly required. Broadcast FM is in the 2-3m range, meaning a full-wavelength antenna would be aproximately 3m in length, we don't even see this on vehicles; most are limited to less than 1m. Even with aerial whip antennas for home-based hifi/stereo systems, often the antenna is not any longer than 1m/3ft, which is about 1/3rd as long as it should be for optimal signal.
The issue here isn't one of having the space for the antenna, since smaller antennas are used in all sorts of applications, such as with FM and vehicles/stereos etc. The issue is having enough antenna to produce a signal strong enough to differentiate from background noise. The signal to noise ratio is key here. Historically, the only good way to get more signal is to use a better tuned, larger antenna, or an array of the same, this isn't so much the case anymore. There's plenty of antenna designs that are still fairly omnidirectional, that can enhance signals. Combine that with more advanced filtering and pre-amplification, a large antenna is not generally a requirement anymore; even the 1m/3ft whips used on cars are often overkill for what we can do with signal processing and modern design. Look at any modern vehicle, and with few exceptions, there's no longer a visible antenna. That's not because there isn't an antenna for FM, it's because the technology has progressed enough to be able to use much smaller antennas to accomplish the same task. The antennas are still there, they're just so small and well placed that you don't need a flagpole on your hood or trunk lid to have it work as-well-as any other FMrx antenna.
Given that the proposal requires a minor redesign of the cellphones to incorporate the broadcast receiving radio, adding a small antenna, or simply using the chassis of the phone as an antenna, would not only be possible but it should be fairly trivial to accommodate for. by no means am I saying it would be the worlds greatest FM antenna system, most certainly it would not be, but it should be sufficient to differentiate the signal from the noise; with relatively trivial signal processing, it should be more than adequate for the purpose.
The technology surrounding FM broadcast radio didn't just cease and we get what we get; vehicles, among other specific technologies still utilize FM radios and development has continued on them even though very few people have been watching. The technology is far improved from what you can build with a battery, coil of wire, a speaker, and a handful of resistors/capacitors/etc. and similarly it's far improved from what vehicles had even 15 years ago. Add that to the fact that radio technology is all pretty much the same across the board (from what we use for broadcast FM, to WiFi, 4G/5G/LTE cellular, and GPS included), and a lot of the developments made in any area of radio can be almost directly translated to another radio on a different band, and there's a lot of technology that, unsurprisingly, will blow most of what most of us have in our houses on our hi-fi stereos, out of the water.
The wonderful thing is that a lot of it is tied to miniaturization and modernization of the technology, meaning a lot of this is tied into integrated circuits that are being mass produced already. IC designs that can be embedded into other ICs to decrease the overall number of chips in a device, fairly easily.
The point I'm dancing around is software-defined radios. SDR is becoming a huge player in all aspects of radio technology, and can replace far more advanced/complex systems with something less complex than a raspberry pi, and often less costly. The big cost of SDRs is mainly regarding transmission, since they don't put out a very strong signal, and need some significant and high-quality amplification to be useful; but we've seen SDR chipsets starting to dominate the lower-cost market within the HAM/Amateur radio space. Extremely capable, very small and power efficient radios, for significantly less cost than more traditional methods of doing the same. The issue is that first word: Software. With great software comes great responsibility.... or something. Fact is there's a lot of SDR radios out there with garbage software interfaces.... at least there are right now. Things are improving all the time. The wonderful thing about SDR, is that they're generally compatible with whatever you want to use them for... meaning AM/FM, or even something more elaborate like OFDM, or other modulation techniques. This means these radios can essentially be re-programmed on the fly to adapt to a new standard with little more than a software update.
I apologize for the long discussion on this, but the technology is so interesting to me the more you look at it. Yes, antennas are important, but not nearly as important as they were even 10-15 years ago.
I've noticed that some sellers seem to list the same item a number of times.... I'm sure not all of them are for unique items.