From the 3.5 days, Wizards has pulled a 180, and made magic items completely optional in 5th edition. This design choice was even indicated in their publishing schedule, as the Player's Handbook saw release many months earlier than the Dungeon Master's Guide, where nearly all magic items were included. Early adopters to the game know well that magic items are at least tertiary in the system.
This, of course, poses some new challenges that DMs might not be aware of. For example, because magic items are not strictly necessary to play the game, and because magic items almost always provide a benefit without some sort of trade off, they can significantly increase the power of a party. This means that to provide an even challenge to the party, you'll have to provide more challenging monsters, and you'll take a ballpark guess as to how much more powerful the monsters should be. If a DM is not aware of this, monsters of appropriate CR are going to get stomped, and your players are going to get bored.
Moreover, there's no hard and fast ways to spend gold on magic items, as there were in previous editions. This is intended to reinforce that magic items are ancient masterpieces, and that they are not simply bought-and-sold as normal items are. However, his assumption can mechanically limit what is possible in many campaigns, where magic items might be more common (we're looking at you, Eberron!)
Rarity vs Power
In 5e, magic items are organized by rarity, a system that has its advantages, and a few confusing disadvantages. The most powerful items are Legendary or Very Rare, whereas the least powerful are Common or Uncommon. This is nice because it highlights mechanically that 5e doesn't intend for the world to be overrun with magic items. A powerful item might be unique, or at least one of a very few number; commoners don't have rings of invisibility.
On the other hand, it's a bit problematic that an item's rarity is always tied to its power. What if an item is unique, or even outright bizarre, but isn't necessarily powerful? Plenty of interesting magic items could be written uniquely to fulfill a role in your campaign, but it seems incorrect to deem a unique item Uncommon if it isn't that powerful, since that word implies there are quite a few of them in existence. The same problem arises if you decide that a powerful magic item is abundant in your campaign. 'Power' and 'Rarity' need not be in lockstep.
A Better System
If you campaign is going to mess with the intended rarities of magic items, a good solution is to simply replace the 'Rarity' of an item with an equivalent 'Power' term.
Common = Lesser
Uncommon = Minor
Rare = Medium
Very Rare = Major
Legendary = Legendary
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