I'm not a Google employee (this is a user forum), so I don't have an inside track. So anything I say is just my impressions from discussions plus statements from a few years ago when this change happened, and in no way an official explanation.
Firstly, external storage isn't disallowed, it's just installing apps to external storage that isn't supported.
So there's no problem with using cards as media stores, and some apps also allow you to store their data files there (useful if you use e.g. offline maps, which can get rather large).
But it would be fair to say that Google are not fans of removable storage at all. They would say that it's slower and less reliable than built-in storage (both true) and that it confuses users (debatable). So their preferred model is significant internal storage, all of which can be used for apps, data or media without you having to worry about how much "app storage" or "media storage" you have, and this "unified" storage has been the norm since Android 4.0. And to be fair it does work well when you have a device with a large enough internal storage - better, in my opinion, than the older model of limited internal storage plus SD expansion (and I lived with that for a number of years, juggling apps between internal and external as well as using all of the root-based tricks available, and am happy not to have to do that now).
In Google's vision there wouldn't be any other storage, though they deny actually trying to kill SD cards. If you look at the devices they control (Nexus series) the last one with an SD slot was the Nexus One (2010). Most manufacturers disagreed and kept SD support, but the base OS no longer supports moving apps to SD. Some manufacturers did add apps to SD support back for some of their devices in some software releases, but in general that's the story.
To be honest moving apps to SD was always a bit of a botch. It was really a work-around for the limitations of early Android devices, which had very, very limited internal storage. It only moved part of the app and none of the app data, so you'd still run out of space, just more slowly. More seriously, if you moved an app to SD any widgets associated with it broke the next time you restarted the phone - that is one thing that I could imagine confusing many users. I'm sure it could have been improved, but there would have been costs (e.g. having to reformat SD cards to a native linux format rather than fat32), so I have some sympathy with them deciding that it was simpler to just keep apps in internal storage. Removing the option altogether was less customer-friendly, but Google do tend to just decide how they think things should be rather than worry about what customers might prefer (though they are not unique amongst big tech companies in that).
The other thing you'll often hear people say is that "Google dislike SD cards because they want everyone to use Cloud services". I'm not sure how true that is. Certainly they do want you to use their cloud services, but whether they genuinely try to disfavour SD card use to try to push people this way seems more debatable to me. And since SD cards are still supported for media (which you can stream) but not for apps (which you can't) I don't think that is relevant to this particular decision.
Having used both older devices (limited internal storage plus ability to partially move apps to SD) and a newer one with decent internal storage and no SD slot, I much prefer the latter. But I intend my next device to have at least 32GB storage plus SD expansion, because that is the best match to my own requirements.
