Okay, my tips on how to enjoy the combat are:
1) Play as a Melee DPS character.
Because this gives the most dynamic playstyle (you're always in close, either ambushing mages/archers or in the thick of it), and because of this, you are best able to see what you are fighting. Ranged characters, spellslingers etc don't have to grapple with camera issues as much, but they can often devolve into you firing off arrows/spells at red life bars, not really seeing or registering what you are fighting. I find being in close helps to make the fight more 'real', and makes it feel more like you are engaging actual opponents, instead of just a set of life bars.
2) The AI can be trusted to tank, but little else.
From a tactical standpoint, you should focus on what your mages, archers and other DPS characters are up to, in that order. Mages should be casting barrier whenever it is available. The AI is somewhat capable of this, but frequently casts it on the wrong people, or doesn't see where it would be best used. Archers can do big damage, but the AI is terrible at adjusting its aim when enemies move behind cover. As soon as they lose LOS, they race in to re-establish it, and usually end up blundering into close combat. Try to move the fight into open ground, so there isn't much terrain that can cause this to happen, position your archers and leave them to blaze away.
As for combat DPS, you should control those characters yourself. You are far better able to see and move to trouble hot spots on a moment to moment basis and know what abilties to use, than the AI can. For this reason, a good player will do a much better DPS job than say Iron Bull or Cole will. They simply don't make best use of their time. Tanking is something you can safely leave to the AI, because it involves standing still and being hit - something the AI excels at! At the start of a fight, control the tank, move them into the thick of the fighting, and forget about them until the combat ends. If something dangerous breaks through to attack your archers and mages, its best to just have your DPS fighters ambush them instead. They only need to distract it long enough for you to activate tac cam and get your support guys out of the way.
This may sound like general combat advice, but it makes for a fun fight IMO. Simply put, playing as a support character throwing up barriers etc or being a ranged character firing at health bars that looks like some swords and vague shapes in the distance, isn't very fun. Learn to mitigate the AI's mistakes with archers and mages, and you can quickly correct such things, and concentrate on just racing about, killing stuff in extravagant manner. You'll see what you're fighting, you'll see yourself doing cool moves, and you'll feel like you are making a real contribution to the fight rather than just watching your team do it for you.
3) Try to move through areas without over-levelling too much.
Wanting to complete all side quests etc is fine, but you don't have to do it all at once. Complete all the side quests in an area that feel relevant, but try to leave all the really obvious filler stuff for another time. Not only can it wear you down emotionally, it will lead to you becoming overlevelled and once you break the difficulty curve in this game, it is very hard to find satisfying fights again. I also suggest not using item crafting (I know some people really enjoy it, but the game is already very easy and you just exacerabate this by making ultra powerful weapons). The game has a real problem when it comes to difficulty, and you have to meet it halfway, by not overlevelling too soon. Keep cycling through the various areas, so you can at least experience some fights against all the various foes before you blow right past them and just consider them a joke.
That's all I can suggest anyway. I really don't think this game is much fun if you play it as a tank or mage etc. Mages were fun in the previous games, but their spells are so one note damage dealing and defence in this game, that it just doesn't feel... well, magical! A 2-handed warrior or dual dagger rogue is the only real path to satisfying combat IMO, the reasons I've outlined. The game is very flawed in its combat I agree, but it isn't a total loss if you try to work with the game and play to its strengths.