It doesn't disallow the rune knight from putting runes on ally's equipment, or giving inscribed equipment to allies, but there's also the difference of language from Artificer infusions, with infusions, it refers to "the wearer," and rune knight refers to "you." So it seems that it wouldn't work.
Can a rune knight inscribe allies' equipment and have them benefit from the runes?
Best Answer
It can only be your gear and only you benefit
The description of the primary Rune Carver feature says:
I admit that the wording that comes later merely says you can choose a number of objects equal to the runes you know, without stating it can only be your equipment. But the description of each individual rune makes it clear that only you can use the rune or benefit from it anyway.
For example, the Fire Rune says:
and then:
There is an argument that the previously mentioned paragraphs can be taken separately, in which case you could put a rune on somebody else's weapon which would prevent you benefitting from the first aspect (the proficiency bonus) but could still activate the rune when you hit with your weapon (even though the rune is on somebody else's weapon)...but that would be rather pointless! (And doesn't seem to be the intent).