What are the most important things magic items do for the players into higher levels of the campaign?

Question

Currently I am planning for a campaign that might essentially end up with no magic items, and I wanted to get an idea of how that tends to effect game balance with the PCs. The previous campaigns I've played (which are also the only campaigns my players have also played) have never gone past level 9, and didn't really include any magic items and often had their own custom creatures, so I'm not exactly sure how their presence actually tends to alter a game (in the higher levels in particular).

In other words:

What are the most important things magic items do for the players as the game scales into higher levels of the campaign?

This setting boasts some steampunk technology and the players know that I greatly reward creativity, so if I have an idea of what is really missing I can compensate at least some of the essential components and avoid situations where the others arise.

Answer 1

5th edition was designed to not require magical items. A party of level 20 characters can win a fight against a CR 20 dragon with no magical items whatsoever.

That said, one very important aspect of magical weapons is that they bypass resistances and immunities of creatures. Without any magical weapons, a fighter is almost useless against a creature immune to physical damage, unless he has any magical weapon. If you don't give any magical weapons, you can just not use monsters with immunities to avoid the issue.

In conclusion, 5e works just fine with no magical items, so long as the DM is mindful of resistances and immunities of monsters.

Answer 2

Magic items basically do two things: increase numbers, or give features you did not have before.

Both of these affect non-spellcasters more.

Increase numbers

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.

Give Features

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.

Counter Immunity/Resistance

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.

End Result

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.

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^{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.}

Answer 3

Magic items are unnecessary under most circumstances.

Xanathar's Guide to Everything page 136 addresses this question fully and directly in the following sidebar (emphasis added):

Are Magic Items Necessary in a Campaign?

The D&D game is built on the assumption that magic items appear sporadically and that they are always a boon, unless an item bears a curse. Characters and monsters are built to face each other without the help of magic items, which means that having a magic item always makes a character more powerful or versatile than a generic character of the same level. As DM, you never have to worry about awarding magic items just so the characters can keep up with the campaign's threats. Magic items are truly prizes. Are they useful? Absolutely. Are they necessary? No.

Magic items can go from nice to necessary in the rare group that has no spellcasters, no monk, and no NPCs capable of casting magic weapon. Having no magic makes it extremely difficult for a party to overcome monsters that have resistances or immunity to nonmagical damage. In such a game, you'll want to be generous with magic weapons or else avoid using such monsters.