It is worth noting that the artificer has the same wording listed in its class description of similar ability. Mainly important because it was released much later so at the very least, it is unlikely to simply be an error.
You ignore all class, race, spell, and level requirements on attuning to or using a magic item.
However as for Actual applications: One case I can find that might relate to it is spell scrolls:
If the spell is on your class’s spell list but of a higher level than you can normally cast, you must make an ability check using your spellcasting ability to determine whether you cast it successfully. The DC equals 10 + the spell’s level. On a failed check, the spell disappears from the scroll with no other effect.
The reason I mention might, is that it doesn't directly reference character level but rather spell levels, which are attained at higher levels.
Unfortunately There isn't a solid answer on if rogues are meant to be able to use spell scrolls.
Another situation in which character level might be applicable is the Holy Avenger
While you hold the drawn sword, it creates an aura in a 10-foot radius around you. You and all creatures friendly to you in the aura have advantage on saving throws against spells and other magical effects. If you have 17 or more levels in the paladin class, the radius of the aura increases to 30 feet.
Again, this doesn't say something which is verbatim in the class feature. However, clearly having a higher class level affects USING this magic item. Remember the description mentions "requirements on the use of magic items." However, this requirement isn't a requirement for use, but rather more of a requirement for additional features.
In conclusion: If you interpret the rules broadly, this part of the class feature will enable greater use of some magical items.
However, it appears there are currently no direct requirements related to levels on magical item use in official published 5e material. The DMG even specifically suggests avoiding adding attunement rules. Another note is that monsters (or npcs) typically do not have levels (spellcasters are often specified however) so any magic item with a character level requirement would create a conflict in usage between NPCs and PCs.