Magic items basically do two things: increase numbers, or give features you did not have before.
Both of these affect non-spellcasters more.
A Longsword +1 increases your DPR (Damage Per Round) around 15-20 percent, depending on your Strength. Less for Paladins after they have Improved Divine Smite, more for Fighters, as they do not have other means to increase damage.
A Wand of the War Mage +1 increases Wizard DPR around 8%, as it does not provide bonus to damage, only for attacks. It does not help with spells needing saving throws, and most spells do require saving throws instead of attack rolls, so you can approximate a Wand of the War Mage to be around +3%.
As you usually can not cast more than one spell in a turn, having more spells is not as important as casting the existing ones in a more powerful way. Quite a lot of casters end the days with remaining spell slots.
An Assassin Rogue can never fly on his own, or breathe underwater. A Winged Boots or Broom of Flying is a big deal for him, but not so much for a Sorcerer.
A few lowly Wererats can completely wipe out a high level party of Rangers or Rogues without magic weapons, just because they are immune to non-magical weapons.
Cantrips are usually much weaker than weapon attacks, and as the levels go up, the gap widens. In exchange, spellcasters get more powerful spells, and more spell slots. Basically the base damage (effectiveness) of spellcasters is lower, but they get way higher spikes, in the form of area damage, control, or buffing. Magic items help them much less.
If you add magic items to the game, the game balance will change significantly.
Fighters, Rogues, Rangers, Paladins, Valor Bards and Monks get stronger, while Wizards Sorcerers, Clerics, Lore Bards and Druids get weaker, relatively. Warlocks are a unique combination, they remain about the same power level.
This will not make the game unplayable, but you should be aware of how it changes class dynamics.
While the game claims that magic items are optional, most official adventures are full of them. It seems having magic items is the real default.