There are many conflicting requirements:
- gain of the antenna
- size of antenna
- directionality of antenna.
To make antenna efficient you want it to have a narrow beam to direct most of the energy to the satellite. This implies your antenna will be highly directional. For a hand held device it is almost impossible to aim the beam reliably when the device is held by a unstable platform (your hand), plus the satellite might also be moving. This is why Iridium went with a omnidirectional antenna and it's a pretty big one. Because of the omnidirectional antenna the gain is relatively low, plus the limited power of hand held device, Iridium is forced to use a very low orbit. But you can still use Iridium when you are moving around.
With 5G and mmW on the way, things changes a little bit. Thanks to the advancement of RF technology and short wavelength of mmW, right now it's actually quite feasible to implement directional antenna and beam forming (electronic beam steering) so 3) is somewhat less of a problem because active satellite tracking is possible now. This new development is reflected by SpaceX's Starlink project. A distinguishing feature of Starlink is the usage of beamforming to allow for a highly directional antenna, enabling high bandwidth service.
But if you look at Starlink's receiver the antenna is still 10x of what I'd like to see on a hand held device. In some way I think it's worse than Iridium because it uses a disk antenna for 2D beam forming, rather than a omnidirectional pole. If you shrink the antenna 10x then you need to bump the frequency 10x into the 300GHz range, which is more like infrared laser than microwave. I really don't see that feasible for commercial end users in the next decade or two.
I guess in the near and far future we won't improve very far from Iridium and Starlink. For highly resilient low bandwidth application, e.g. text and voice you use Iridium in the hand held form. For high bandwidth usages you place a satellite internet hotspot on a decently stable platform, of the size of a pizza box, then pass through the connection to the user device via WiFi. I'd say this is good enough.