Usually, Not Much
As you've realized, the artificer class has somewhat strange requirements that seem more specific than necessary. At low levels, it really doesn't matter whether you're using artisan's tools or a normal focus. At high levels, you have a lot of options that are superficially similar with minor differences. These can probably be reasonably flattened with little to no mechanical impact.
...Unless You're Multiclassing
This is really the main balance implication that I'm aware of. Having played specifically an Artificer/Wizard multiclass build, I can also say that it's not exactly a small one.
You require artisan's tools to cast your artificer spells, but those cannot be used to replace the material components for your wizard spells. Further, the spellcasting foci gained by the artificer subclasses are also restricted to artificer spells (and I would argue that the infused items implicitly are as well, since they're replacing the tools).
This conflict imposes real costs on certain Artificer/Wizard multiclass decisions, especially one which wants to dedicate one hand to a shield. You're pigeonholed into finding something that can work for both. Enhanced Arcane Focus is great for this, but it uses up an infusion slot, and you will likely come across things you'd rather be holding with that hand.
Otherwise, you're left with doing complicated action economy things like sheathing your tools one turn to use a component pouch, and hoping you won't need to cast a spell as a reaction before you can draw them again.
...But Even Then Only Sometimes.
This is all very frustrating, until you get to artificer level 5. Now suddenly even magical arcane foci are on the table, and you have your infusion slot back.
But is getting to artificer level 5 desirable? For my purposes, a three level dip gave me everything I wanted from the class, while keeping eventual access to 9th level spells in a campaign that would someday hit 20th level. Pushing to level 5 for just this convenience is also not a trivial decision.
So, Maybe. Sometimes.
This is the only place I'm aware of where there is a severe mechanical impact to the distinction. Like so many things in D&D, it's extremely contextual. But in my circumstances, your simplifying ruling would effectively give my character an additional infusion slot back, and the ability to gain stronger spellcasting foci indefinitely.
Remember, this isn't a hypothetical. This is a particular character build that does exist, that would gain substantial mechanical benefit from your ruling.
Does that matter to you? Honestly, probably not. Dungeons & Dragons has so many contextual mechanical interactions that even if a rules choice unbalances some of them, it's extremely easy to just never encounter them in a campaign. If you aren't multiclassing, you're probably fine. Even if you are multiclassing, you're probably fine.
But artificers are a complicated class, with a lot of options, and giving them more options does have consequences. For someone. Somewhere.