There are four fundamental problems with that approach (though they are not even close to strong enough to render the approach invalid):
- It is more systematic than the actual rarity of official magic items
seems to be, and official items may not follow it very strongly
- It attempts to balance items from an overall game-mechanical
perspective, which given the above point is not very precise
- It is far less reliable for any item which is not a weapon or piece
of armor (it's easy to compare +1/+2/+3, attunement requirements, and
cursed-ness, but often not so easy to compare more varied effects to
one another), and is very imprecise in comparing distinct magical effects
- Rarity is useful for classifying items in a variety of ways (such as
random treasure tables), but is mostly an inert piece of information
In short, that approach to balancing is convenient and fast for a specific subset of magic items, but is much less precise than its systematic approach suggests. In that sense it is much like CR calculations for encounters (especially if they include custom monsters!). It provides a vague guideline, but is not a good enough standard that deviating from it makes your prediction necessarily worse. Deviations may make it much better!
So with those in mind, I'll pose this slightly frame-challenging question:
What will you be using the item rarity for?
If you're just looking for a guideline on how much a magic item should be worth in gold, this approach seems like a fine one. I offered some magic items for my players in a campaign I'm currently running, and some of them I wanted to restrict until later in the game to avoid making challenges too easy. A level-appropriate reward for that point in the campaign would have been one common or uncommon magic item, and consequently item rarity was a pretty handy guideline to use.
But that approach wasn't perfect. One of my players got a Broom of Flying, which is uncommon, and has also posed huge balancing challenges. Not insurmountable by any means, but definitely in the vicinity of the kind of thing I wanted to avoid by sticking with common and uncommon rarity. Another player got a +1 weapon (also uncommon), which has been very, very easy to balance mechanically as its magical properties are clear and limited.
Another player wanted a custom magic item with specific properties. These properties are useless in combat and largely undefined in terms of impact on the plot, so I decided it was appropriate without any special calculations-- it made the game more interesting without making it much easier, so the rarity (however defined) just wasn't much of a factor.
So, that's my assessment of Lino Frank Ciaralli's approach: quick, convenient, and sufficient for specific uses of item rarity categories. If it suits your needs for a given purpose, then it's great! But if you're trying to use it for other purposes, it might be totally mis-specified.
The uses of magic item rarity category are few but diverse, and so a given method of determining that rarity won't have a general-case, in-a-vacuum solution that is inherently problematic or problem-free. Such a thing can only be evaluated in light of a specific outcome you are hoping to achieve.