Magic Items are secondary to the design of 5e
In a tweet, Chris Perkins said
If your 5E characters have no magic items, the game would still be
balanced. Magic items are pure candy.
The designers created D&D 5e to be able to function without assuming characters have magic items, and magic items do not appear in the Player's Handbook (Though some of them appear in the Basic Rules)
Thus, magic items are typically not as carefully balanced as other aspects of the game, they are an optional rule.
Magic Item Power Level is Largely Inconsistent
There is no guarantee that a magic item's rarity will give you any indication of how powerful it is, and items within the same rarity are not necessarily balanced or consistent with each other. Consider the Staff of the Python, an Uncommon magic item that is considered to be incredibly overpowered:
You can use an action to speak this staff's Command word and throw the
staff on the ground within 10 feet of you. The staff becomes a giant
Constrictor Snake (see the Monster Manual for statistics) under your
control and acts on its own Initiative count. By using a Bonus Action
to speak the Command word again, you return the staff to its normal
form in a space formerly occupied by the snake.
And, the more important section:
If the snake is reduced to 0 Hit Points, it dies and reverts to its
staff form. The staff then shatters and is destroyed. If the snake
reverts to staff form before losing all its Hit Points, it regains all
This means if you use your Bonus Action to recall the Snake, you can infinitely replenish it's hit points, of which it has 60.
Compare the potential utility of this item with the Cloak of Elvenkind, which makes you better at stealth, and consider these two items are of the same rarity.
All this being said, there is a good case to be made that the Arcane Propulsion Arm is aptly placed, and consistent with other options in the Very Rare tier.
The Arcane Propulsion Arm is essentially replicating a 7th level spell
The Arcane Propulsion arm acts as a prosthesis for a creature missing a limb, it improves upon the Regenerate spell, which states
The target’s severed body members (fingers, legs, tails, and so on),
if any, are restored after 2 minutes. If you have the severed part and
hold it to the stump, the spell instantaneously causes the limb to
knit to the stump.
This makes the Arcane Propulsion Arm consistant with other magic items in it's tier, namely, the Amulet of the Planes,
While wearing this amulet, you can use an action to name a location
that you are familiar with on another plane of existence. Then make a
DC 15 Intelligence check. On a successful check, you cast the plane
shift spell. On a failure, you and each creature and object within 15
feet of you travel to a random destination. Roll a d100. On a 1–60,
you travel to a random location on the plane you named. On a 61–100,
you travel to a randomly determined plane of existence.
This item is also Very Rare and replicates a 7th level spell.
Also consider the Spell Scroll chart, and note the rarity of a 7th level scroll.
At least in this case, an item that can essentially cast or emulate a 7th level spell should be considered Very Rare.
This being said, the Prosthetic Limb from Tasha's Cauldron of Everything is considered Common, another point in the favor of the rules and rankings of magic items being inconsistent.