The game isn’t shallow. There is no more or less luck than in most other miniature games, though you can get wrecked by bad luck as you could in any dice-based game.
However Test of Honor’s mechanics make it badly suited to play for attrition, so you should always play for a scenario, unless you want the endgame to turn into a supremely unfun slugfest.
Unfortunately, the official scenarios tend to be rather simple and / or lack balance, so you should simply steal and adapt scenarios from other games, or even make your own.
As William said, there are also some balance problems when it comes to army building (imho mainly cavalry and muskets being on the low end, and bows, spears and naginata on the high end), but that’s not a problem since the game has no competitive scene. You should just play what you want or houserule the main offenders.
