No. Really. Read the darned feature. As written (bold mine for emphasis):
"You produce your artificer spell effects through your tools. You must have a spellcasting focus—specifically thieves’ tools or some kind of artisan’s tool—in hand when you cast any spell with this Spellcasting feature (meaning the spell has an ‘M’ component when you cast it). You must be proficient with the tool to use it in this way. See chapter 5, “Equipment,” in the Player’s Handbook for descriptions of these tools.
After you gain the Infuse Item feature at 2nd level, you can also use any item bearing one of your infusions as a spellcasting focus."
So - You must have a spellcasting focus (as opposed to other classes, who can cast spells without a focus if they don't have a material component). For this class, thieves' tools or some kind of artisan's tools are foci (instead of the usual arcane focus choices of wand, staff, rod, orb or crystal). Once you reach 2nd level, an item with one of your infusions can also be used as a focus.
If you absolutely, under all circumstances, needed the tools as a focus, there would be
NO POINT to having an infused items as a focus! There is nowhere in the rules where having two foci at once is beneficial. How can this be a RAW vs RAI thing? What, then, could possibly be a different intent for that last sentence?
Enabling an infused weapon as a focus is totally part of the intent for the class. Don't sweat it.