Cameras still use media. While a smartphone might save pictures to the cloud, even a low-end machine sold as a camera uses memory cards. The Sony α6000 shoots 10 frames per second with 25 MB per (raw) exposure, which means that you will not only greatly exceed bandwidth availability but will chew through many gigabytes of memory cards.
At an "event", the wireless bandwidth may be seriously overcommitted by the large crowd all trying to use it at the same time.
So, a smartphone-based device might be specialized for journalism. It can record stills, video, and audio and take notes, at high bandwidth production and still operate while being cut off from the network. When you snap a photo at a concert you want the file to save, immediately, not jam up while trying to get through to the server.
It is important that the chip be easily swappable so it can be changed when full and possibly sent by courier to another user, whether it be an editor in a professional situation, or just so the wireless transfer of backlogged data doesn't take a ridiculously long time.
Removable cards will be a feature for pros, and prosumer usage. Perhaps many dSLR users today, non-professionals, don't remove the memory card when they get home but trigger a wireless transfer while recharging and putting things away. But I don't see the feature of an easily accessible card slot going away.
Maybe a high-end smart device that's more phone than camera will have a memory card slot that can be swapped without cutting power and rebooting though not especially easy to access. That is, peel the shell open after removing from the case, rather than having a handy door.
You can lampshade it by explaining to the receiver that yes the device does have a place to put cards, as high-end devices will.
media in general
I store my photos, work, backups, etc. on a local file server. Enterprise storage locations exist and when you use the "cloud" that's where it is really stored physically. So media exists even if you don't use it directly normally.
A bare HDD is not meant to be a removable media unit. But it is! I buy bare drives and use a dock in the manner of a cartridge reader. It's a sealed box with connectors for power and data. A "card" meant to be used as removable media is exactly the same thing. With easy to use connectors, the only difference between "media" and internal storage units is the durability and care needed for handling. A bare drive might not like even being placed on a hard table in a less-than-gentle manner, but travel drives put shock absorbing material in a case around it and adapts the manner of connecting.
So if media exists even if only for use in the cloud-based storage system, it will be possible to adapt it to portable use as a secondary market.
If devices have no provision for physical media or connections at all, you can still have a separate little box running owncloud with a personal networking protocol. So it doesn't plug in physically, but you still have a little box that must touch-to-pair and then remain within 10 meters to use. The pairing process gives you the plug-in event to acknowledge in the story.
Same thing as a card. Just wireless.
It overcomes the media-free nature and is exactly what solutions would emerge for this need.
Such a box doesn't have to be orders of magnitude larger than a phone, e.g. holding a 3.5" drive. There will be local storage designed for tablets and laptop-equivalents, with more substantial storage size than the casual phone-like device. That can be packaged with the most minimal mobile-device chip (basically a speck) and battery to form a personal cloud server.
If the purpose of the product — which is developed separately from any phone — is for portability and hand-off-ability rather than capacity, it might be very small. It might be as small as a data "card" and serve the same purpose, but be wireless and not need any slot!
It could work with a phone case to hold it close without losing it, and keep it powered. This would be after-market, not affect the phone design but overcome it, and is something a hobbiest could hack together today. The tiny wireless server is "internet of things" brain.
Such products will exist, no doubt. Even if niche or unusual, or even customized, they could get one ideally suited for their purpose.
The future you describe, besides being media-free, also provides for highly customizable products. Even today we have at-home surface mount circuit board makers and 3D printers. So, even without a specific hobby industry for emerging "iot", imagine someone salvages a chip from a "thing" and adds a storage chip and programs it with encryption etc. He cobbles together a personal cloud server and it's the size of a matchbox.
An advantage to this is that it's not limited to just memory. It could contain special functions that you wanted, as hardware.
..."OK, how do I install it?"
She was expecting to be told a URL for a private package store, for an app not found on the vendor-approved store. Most likely a QR code displayed on Alice's screen, or even a bump-file transfer but that generally can't copy apps. Betty never installed any app that wasn't from the official "store" listing, so she wasn't sure what would happen next.
However, Betty was definitely not expecting to be handed the app in a little box! How silly, like a joke a little kid would make, crossing the lines between cyberspace and the physical world.
On second glance, the package — about the size of a matchbook— bore the livery of a popular game company. "Is that a game booster? I've never used one" Boosters were for young men with too much testosterone who played first-person shooters and wanted life-like fidelity in rendering huge multiplayer meelies. It made the phone or tablet run faster and have better graphics; that's all she knew. Some were for specific games and were tied with company-specific features. Maybe that's the idea.
Indeed, Alice explained, "Connect your phone to this. The label is just a disguise: it's been reprogrammed to [[whatever she was talking about]]. It holds your secret files on a personal cloud server and you connect only over the personal peripheral network [[bluetooth? ]], so the files are never seen on the open network between devices. It also implements [[special features]] she added with a wry grin.
Betty turned it over in her hand and looked it over, spotting the pairing icon on the top of one of the small faces. "Stick a toothpick in that hole", over the icon, Alice indicated, "and then touch the pairing spots together." She initiated pairing the devices, and Alice then typed a ridiculously long password on Betty's phone and worked the toothpick again with what appeared to be another secret code. The icon on the "booster" flashed green, and an app-install acceptance window appeared on Betty's screen.
Alice had a seemingly cryptic smile that she tried to hide. "Now it will work only on your phone. If anyone else tries to pair with it, your saved files will be hidden as if nothing was saved on it; it will say it was factory-reset and wiped, but really they are safe and will return when you re-pair it with this device.
Betty hoped she didn't have to replace her phone while this was going on; certainly Alice had that covered too. But she didn't bring it up; this was already too complicated. But she did need to know: "What about power?"
"Use the same universal charging pad as all your other devices," said Alice as if it was perfectly obvious. Indeed, the charging logo icon was embossed in one of the faces of the "booster". Betty didn't have any other fancy devices; an earpiece never appealed to her and people she knew kept losing them anyway. "I just have the stick-on dot that came with the phone."
"Well, you'll have to go buy one. The charge will only last a day or two, so don't put it off." Betty, impatient with the un-geekiness of her friend, gestured towards a row of vending machines.