Because Achilles didn't wear a pair of magical gauntlets, a magical cloak, a magical pair of boots, a magical sword, a magical suit of armor, a magical shield, a magical spear, a magical tunic, 2 magical rings, a magical neckalce and 2 ioun stones.
It also never explicitly stated that Achilles ever went to the toilet, much like 95% of fictional characters... It's just not normally important to their story to know they had a poop before the final showdown, doesn't mean they don't do it.
It could be that he had a bunch of minor trinkets that weren't really worth focusing on. Perhaps his gear was a cut better than that of the average soldier? In DnD terms it might well have been that above list - just none of it was nearly as important or interesting as the actions of Achilles?
Same applies to many fictional heros - they may have had a few bits of anonymous but well made equipment - does it matter to the story?
One option I used was to make most weapons and armour 'non magical' - they're just more extreme versions of masterwork... that suprisingly cost about the same as their magical equivalents. Some enchantments can also be treated this way - keen, ghost touch, vorpal and other non visual stuff is easy. Some are harder to work in, but even 'showy' stuff like elemental types could be the result of strange materials rather than magic?
We coupled this with some 'items' as innate powers - stat, ac and save boosts mostly.
Reserve special history backgrounds for the one or two powerful genuinely magical treasures each hero has.
Removing some of the more physics warping effects can help with the imagery. Ioun stones = cloak pins. Make bags of holding, flying boots and the like rather rare. Etc. Etc.
They still work much the same as the 'suggested wealth' characters, but the all important descriptive aspect of the game is subtly different?
YMMV but I found this made the game feel much less 'about the items' and far more about the powers of the PCs, while changing very little of the mechanics (apart from craft rules) or encounter balance.
Has some slight effects in that you can't supress some items with antimagic/dispel any more and most 'magic item' creation was done by craftsmen instead of wizards. But nothing really problematic.
If the problem is with the PCs having powers at all, rather than the source of them, then this really isn't going to help!
As far as the magical changes to society.
Likewise, from a descriptive angle again, cutting down the number of magic users from the DMG guidelines can make for a less magical feeling world. Instead of few % of the population being spellcasters, perhaps there are only a handful in each kingdom? Just happens that some of these are PCs.
Perhaps the gods only bestow powers on a few 'miracle workers' (clerics) rather than most of the clergy. Maybe these powers only work on chosen individuals (players, villans and major npcs) - no mass curing of plagues or clerical army units? Things are exactly the same for PCs, but it changes the backdrop?
Possibly apply something like Sephulcrave did in his excellent story hour. Mages don't meddle in politics - it causes way too many problems. If they get caught, then other mages will band together to stop them... again this would massively lessen the impact of magic on society, but still keep it with very minimal rules changes?