It would be really cool to be able to add new recipes using CubeJS as an alternative to CraftTweaker.

Apparently, CubeJS can change every JSON based recipe, just as CraftTweaker does. So, this was, in fact, an unnecessary suggestion! I'm closing this.

CubeJS example, for adding drying rack recipe:

event.custom({
  "type": "stone_age:drying_rack",
  "ingredient": {
    "item": "minecraft:grass"
  },
  "dryingTime": 1200,
  "result": {
    "item": "stone_age:dried_grass"
  }
})