How do the Artificer infusions work?

One of my players is running an Artificer and has just reached level 2. Reading the infusion rules we are both a little confused as they seem to contradict.

Infusing an Item Whenever you finish a long rest, you can touch a nonmagical object and imbue it with one of your artificer infusions, turning it into a magic item. An infusion works on only certain kinds of objects, as specified in the infusion’s description. If the item requires attunement, you can attune yourself to it the instant you infuse the item. If you decide to attune to the item later, you must do so using the normal process for attunement (see the attunement rules in the Dungeon Master’s Guide).

Your infusion remains in an item indefinitely, but when you die, the infusion vanishes after a number of days equal to your Intelligence modifier (minimum of 1 day). The infusion also vanishes if you replace your knowledge of the infusion.

You can infuse more than one nonmagical object at the end of a long rest; the maximum number of objects appears in the Infused Items column of the Artificer table. You must touch each of the objects, and each of your infusions can be in only one object at a time. Moreover, no object can bear more than one of your infusions at a time. If you try to exceed your maximum number of infusions, the oldest infusion ends, and then the new infusion applies.

If an infusion ends on an item that contains other things, like a bag of holding, its contents harmlessly appear in and around its space.

My question is this, the fact that Infusions last indefinitely until either the Artificer dies, places the same infusion on a different item, or loses the knowledge of that infusion I take to mean that over time an artificer can have every infusion running on multiple items.

For instance the artificer knows 6 infusions, day 1 he casts 1 and 2 on his armour and a weapon, day 2 he casts 3 and 4 on a different party members equipment and day 3 he casts the final 2 on a different party member. Is this the right application of the rules, to me it makes sense otherwise what is the point of having a class that makes magic items?