ad_hoc
(they/them)
My group play tested the HELL out of 5e, and it was apparent early on the magic items were not necessary, but also unique. Gone were the 3e days where you have a bucket of +1 Longswords. Our first campaign for 5e was played with scarce magic items. I had a +1 Longsword that shed light like a torch. It was my one magic item until 3rd level when I got a holy mace that did +1d6 extra radiant against undead and fiends. The game worked great. We played until 9th level with scarce magic items. I never got rid of my two magic weapons, and even though I started as an Archery Fighter I eventually took TWF to complement my two magic weapons. It's pretty amazing, to be honest.
Our next campaign was played with high magic living through a Fiendish Apocalypse. All of us had lots of magic weapons, items, and armor, looted from corpses of dead heroes and villains. The DM wanted to see if we could play a Monty Hall game and how the system would handle it. All of had several legendary items and no room to attune more. The way the DM handled it was he increased the CR by 1 for each legendary item we had attuned as a group. To keep the Exp down but the CR up he'd sprinkle in a few extra Fiends for every encounter. The great part about 5e is low level monsters can still be effective, even against very high level PCs. That's a big departure from 3e where you can't field CR3 monsters against a 16th level party and expect anything out of them.
Wait, that's your idea of scarce items?
In my games players can get to 5th level without any permanent items depending on how the rolls go. In my current game the party is 4th level (almost 5th) and have a single magical robe among them. That's normal for us and I think 5e in general.