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.