The elephant in the room
Even if "high def" audio recordings are any real improvement on CD, you're not going to notice the difference unless your reproduction gear is up to the job.
Hardly anyone has audio reproduction gear that counts as "top notch hi-fi" by the standards of the 1970s, let alone kit that's better than that. So for most people, even if "high def" recordings do provide a potentially detectable improvement, it's not going to be apparent on playback.
So what's it all about, really?
The article's point about the poor quality of many CDs is a very good one. If these "high def" audio types really wanted us to have access to decent quality music, they'd be concentrating on producing well mastered CDs which weren't mucked up with dynamic range compression and other nasties.
But of course that's not what "high def" audio is about, is it? It's really all about selling a dream and making money from people who can't tell the difference between impressive looking specs and genuine high quality.
A couple or four other points.
Oversampling to increase the apparent sampling rate from 44.1kHz CD standard has a real engineering benefit: it means the DAC designer can easily come up with circuitry that gives greater rejection of unwanted frequencies with less distortion of all sorts, thus producing a higher quality analogue signal to send to your amp and speakers. But interpolation of a 44.1kHz signal to higher frequencies will give you this benefit without the need for higher sampling rates in the recording - and you can buy stand alone DACs to do just this at moderate cost (I've got one so I can play music from a PC HDD on my proper stereo).
The original article's claim that "Increasing the sampling rate extends the frequency response" is true, but isn't a real advantage since 1) most audio repro gear can't reproduce higher than the 22kHz theoretical max of CD and 2) most human ears can't hear such frequencies, which is why audio repro gear mostly doesn't bother with them. (my ears are nearly 50 years old: when they were much younger, they could hear up to about 22kHz when tested. They can't hear much above 16kHz these days.)
The advantage of 24 bit audio over 16 bit audio is that you've got greater dynamic range available, which is genuinely very useful in the recording and mixing stages.
From the point of view of "final consumer recording" even if your ears are able to spot the difference, you'd need one hell of a listening environment to take advantage of any such improvement - not just top notch repro gear, but nigh on perfectly insulated from noise, ideal echo characteristics, and so on.
From my experience, the reason some CDs sound worse than the "equivalent" LP is because of dreadful mastering of the CD. I sometimes get the idea that the record company has hired the cheapest chimp they could find to crank out CD masters as quickly as possible while paying the proverbial peanuts, and to hell with the actual music.
CDs have astronomically better dynamic range than LPs, which also means better noise figures even before you consider dust and wear on LPs. LPs can just about match CD frequency range, until they get worn - wear which increases noise and distortion. Technically, there's no excuse for a CD to sound worse than an LP. If you've got LPs which sound better than the equivalent CDs, the problem is probably bad CD mastering (or maybe you need a better CD player).
I sent one CD back to Amazon after a single listen: a recently remastered compilation by the original artists which was so awfully done the music sounded like it was bad cover versions by a band which had no idea what the music was supposed to sound like.
Sometimes, you can get a CD which is remixed to be a huge improvement on the original LP. It might not be to everyone's taste, but Roger Glover's 25th Anniversary Edition remix of Deep Purple's 1972 "Machine Head" is a case in point.
And finally, given that the youth of today mostly seem happy with lossily compressed files downloaded and played back on their laptops or tablets (or phones - shudder!), surely just striving to achieve CD quality would be an improvement for most?