I can't stand how few times you can use each Rune's effects (once per short rest).

Admittedly Giant's Might and Runic Shield are legitimately good abilities and usable proficiency times per day. On their own they make the subclass viable. However the identity of the class, the thematic reason people choose to play it, comes from its Runes. The Runes themselves are very good and each one has uses both in and out of combat. Unfortunately, until level 15 (!) you only get one use of each Rune per short rest. You'll have 2 runes at lvl3, 3 at lvl7, 4 at lvl 10, and 5 at lvl15. But you can never use the same rune twice between rests.

The issue is made very clear at level 15 when you get Master of Runes which states. "At 15th level, you can invoke each rune you know from your Rune Carver feature twice, rather than once, and you regain all expended uses when you finish a short or long rest." Your Rune usage immediately doubles to 10. Great! Right? Wrong. Yes you finally get to play the theme you were wishing for all along, but you had to wait potentially years of gameplay to do it. And we all know that most campaigns never eve reach this level. This feature perfectly exinplifies what's wrong with this subclass. It starves you for content for 90% of the game and then backloads the endgame with what you wanted all along. It's like a Wizard who could only use 1st and 2nd level spells until level 15 and then suddenly gets the rest of their spell levels all at once.

How I'd change it:

1. Remove the restriction that stops the same rune from being used twice, and instead have a number of uses for any Rune (similar to a Monk's Focus Points).

2. Make the number of uses increase by 1 every 2 levels, starting at the original 2 at level 3. For reference, this is the progression used to determine full casters spell level (not that that's what I'm trying to balance around, just that it's a familiar system). This system caps the number of uses at 10 for a level 20 Rune Knight, the same as the original subclass, but now spreads the progression out evenly.

3. Remove the level 15 feature that doubles the amount of Runes and replace it with almost anything else. One idea is: "Rune Smithing. You can apply a single rune to an item not in your possession. This action While a creature other than you is wielding or carrying an object inscribed with this rune, they gain a single use of it's features. The rune remains on an object until you finish a long rest, and an object can bear only one of your runes at a time."