As an addendum, one thing I've considered is improving non-magical items. For instance, fine or very fine swords might cost astronomically more, and provide a +1 or +2 or even a +3 to hit and/or damage. This is cosmetic to some degree, because it's essentially taking the mechanics of a +1 sword, and saying it's mundane. And it would require rethinking creatures that can only be hit by magical weapons. But it could reserve magic for the true exceptions.
Spirits might be hurt by cold iron or silver, requiring backup weapons that might be inferior to normal weapons, and this would as true at 14th level as at 1st. Magic-users would be de-emphasized a bit, since mundane but excellent smiths could make exceptional weapons and armor, and seeking out and befriending such smiths could be a plot driver. Elvish weapons might be mundane, yet have certain properties, like striking the noncorporeal undead, and some legendary and lost human cultures might be similar (think elvish and Numenorean blades from LotR, and their effectiveness against wights and Nazgul). Since the Expert rules explicitly deal with the exceptional nature of dwarf and gnome smiths, maybe their weapons and armor are uinque. Potions could be mostly herbal rather than magical, and widely available. Similar with certain other magic items with less ostentatious effects, like elven cloaks and boots. Maybe scrolls as well. But magic items that have explicitly magical powers might require wizards, and be unique in certain ways. This works well with intelligent swords -- all truly magical swords might have their own will. This could even be extended to other items, making them dual-edged. This would spread out the expertise; instead of seeking out wizards for answers to all magical items, you might seek out an elvish weaver to learn of the properties of their cloaks, or an alchemist to learn about reagents that cause transmutations.
For my current campaign, I'm doing something similar. My sop to keeping it "magical" is that things like the +1 weapons are crafted but the process itself requires considerable magic and specific expertise that is closely guarded. The crafter doesn't need to be a spell caster necessarily but they do need to know some "crafting magic" that is peculiar to the thing they are making. Elves making elven cloaks and boots and dwarven smiths was very much a part of that idea. Theoretically, a dedicated player could learn to make a few things, but there is no generic ability for wizards to make any old item a player might want.
That's my compromise for keeping it somewhat rare while still acknowledging that someone made all those +1 weapons that are found.
The idea that there's this clear boundary between the normal world and magic is a modern conceit. After all, medieval people believed smiths sung spells into their work, and we're not talking about exceptional smiths. It's just how it worked. It wasn't only about alloys and temper, there was also something numinous where craft melded into mystery and wonder.
I think a lot of the problem is that modern people think of magic as something extra. There's the world, which by default is normal and perfectly mundane, and magic is this gloss over the top, or a set of cheat codes. I prefer to treat magic as something essential. It's not something extra, it's how things work. Magic is everywhere and in all things, and is part of everyday life.
This manifests in how D&D has treated magic-users and magic items. Only magic-users can create magic items, right? Except... why? Why can't a great smith craft the greatest sword of all time, or an elf weave a cloak so perfectly that it blends in with stone? There's this association with blatant spellcasting, and any magic at all.
I like the idea that there's magic in the blade of a sword, even the less exceptional ones. It may not be much magic, but it's there. And that means that an exceptional smith can make a sword of high pussiance, with no involvement from wizards at all.
For scarcity, I think it makes sense to assume there really are people who are exceptional at crafts. The BECMI weapon mastery system introduced the idea of basic, skilled, expert, master, and grandmaster tiers for weapon proficiency. A similar concept could be introduced for crafts. A basic smith might make a basic sword, if you want a +1 blade, you might need to find an exceptional smith. A +2 sword might require a real master. And a +3 blade might require someone of legendary skill and talent. The same could apply to potions -- simple healing philters might be the province of random travelers or good folk, while a potion of giant strength might require more skill.
That turns magic items into an exercise in roleplaying. There might be only one person capable of making +3 swords in all the land, and if you piss him off, no swords for you. In general, you have to seek out these sources, and over time develop contacts and earn favors.