Guess I’ll have to have another look at Yum, because the name alone still triggers ptsd of when Yum was released. Haven’t had to admin a RedHat system since those days so the trauma has stuck…
As to the topic at hand.
I still used apt-get, apt-cache, and friends, until rather recently, does that mean I qualify? 
I’ve never had speed issues with Apt, probably still the fastest package manager I’ve used. In fact, most of his reasons feel kinda “forced”, or at least more like opinions rather than factual problems with Apt.
Nala is, for the most part, a fancy Apt/dpkg frontend. Neat, if you’re into that sort of thing, but it’s not as mind blowing upon reading the project page as the video makes it seem. There have been plenty over the years (like Aptitude, as already mentioned by Wendell).
Said fanciness seems like it would be liable to break in non-ideal terminal conditions, and I can’t help but wonder how it would perform on a slow terminal.
The history function seems potentially useful, but is no substitute for snapshots, and likely won’t help you if something gets really broken as it just uses apt to accomplish its goals.
It’s also a shame they don’t use native functionality to store this history, but rather a custom implementation. Meaning it’s neither portable nor will it “know” of anything done outside of Nala.
Parallel downloads are rather a debatable topic, and apt doesn’t have them for a good reason, given that it still doesn’t support them by default 7 years later, and that apt-fast isn’t available in Debian’s default repository I assume that reasoning still holds. Whether Ubuntu, or other apt-using distros hold the same opinion I don’t know.
Additionally most people will still be limited by their network connection, pulling more data from the same source is not going to make things faster for them (apt already pulls from different mirrors in parallel)
I disagree with your conclusion. I’d posit Nala is a nice UI for functionality apt mostly already provides, the added extras are either nice to haves (history), or things the apt devs explicitly do not want to support (parallel downloads from the same source), all packaged in a nice UI ( “de gustibus et coloribus non est disputandum”).
Maybe I’d change my opinion after having used it, but the video doesn’t convince.
EDIT: found this, after writing the above so guess they’ve come around on the parallel downloads thing, or they consider that the userbase of this tool will be small enough they can overlook it (an apt dev does call it out as disagreeable per his opinion though, so we’ll see if anything happens should it become popular)
Additionally it’s interesting to note that an Apt dev explicitly mentions undo operations on package upgrades are explicitly not supported by the underlying infrastructure, nuking one of the benefits mentioned, but not demonstrated, in the video.
There’s also mention of a CVE-worthy bug, haven’t looked at that any further though.
Anyway, sticking with my conclusion: interesting tool, and nice UI for those that like it, but not as mind blowing as made out to be.
)