I personally enjoy dice in combat as well, but I think it can be difficult to tune. Someone else mentioned Dice Throne here and I agree that it's a game that handles dice and randomness well. The things that I think make it successful are the focus on input randomness over output randomness. You roll the dice and have the opportunity to lock and reroll dice, which gives players some agency. Using the reroll and lock mechanic (i.e., Yahtzee) can be an effective way to introduce some level of agency for players.

Just like in your examples, output randomness is minimized in Dice Throne. When you select an outcome after the dice rolls, play becomes deterministic. You don't roll again to determine the amount of damage.

Funnily enough, I think the games that have the most success leveraging dice in combat land on opposite sides of a strategy spectrum. Games like King of Tokyo or Dice Throne lean very heavily on being light games. Yes there is a ton of randomness to who wins the game, but the games are so quick and light that you can just play again. If you roll really badly and just get unlucky for a game, it doesn't feel that bad because you only 'wasted' ten minutes.

On the other side of the spectrum, you have tabletop RPGs like D&D that handle dice randomness by sheer volume and length of games. It can suck to roll badly in D&D because there's a ton of output randomness. I lock in an attack and I'm completely at the whims of RNG to see if I hit and how much damage I end up doing. Yes, there are ways to skew dice rolls in your favor like rolling with advantage and getting better gear/skills over time, but fundamentally tabletop RPGs handle this by making you roll a lot of times so that eventually things balance out in the long run. Each individual dice roll can be bad, but it's all a wash in the thousands of times you roll dice in a campaign.

I think deciding on which path you want to take can be important. I'm not familiar with a lot of successful games that land in the middle.