The only instance where Divine Pulse come into active gameplay that I can think of is when player uses it to reroll RNG, which I agree is currently very intrusive. I forgot this at the time, so it was my blunder. However, do note that rerolling RNG is not something new to the series, or even uncommon (I am pretty sure FE12 Lunatic almost requires you to reroll RNG for the final chapter; I think a normal strategy is possible, but so far they all seem impractical.) You are right that the optional part is not relevant to the current topic, but it is something about Divine Pulse that is better than some of the other things I listed, like support gambits: like the greenhouses and grinding, it is easy ignore these things, whereas it is very difficult to ignore combat arts and gambits. Let me reframe it: imagine that now all battle results are completely determined, no matter the order of your action. Under this new Divine Pulse, whether or not the player choose to use it or not they would still have to follow an exact sequence of steps. If this sequence is known, then the map is solved and divine pulse is irrelevant; if this sequence is not known then the only difference between having and not having Divine Pulse is the amount of time it takes to come up with the sequence. This is why I think Divine Pulse is okay. It is like restarting the game, which I think all players already did.
To put it more generally, imagine the ensemble, or set, of all possible board states (all configuration of units and their respective states) of a given map. Call any ordered pairs of board states that differs by only one action a "move". All moves have their initial state and final state. Call any pair of moves "successive" if either: 1) The initial state of a move is the same as the final state of another move and 2) their initial states are not the same and both moves are successive to one other move. Call any set of pair-wise successive moves a "tactic". Any tactic of which moves contain the beginning state and final state of the map (whether a win or a loss) is called a "strategy". Any strategy of which moves contain a "victory" board states is called a "solution". The set of all strategy is the "strategy space" and the set of all solutions is the "solution space". So far we have not introduced RNG. To do so, call the probability that a move is successful the "strength" of that move. The product of the strength of all moves in a strategy is the "strength of the strategy". The sum of the strength of all solutions divided by the sum of the strength of all strategy is the "trivialness" of a map. A mechanics that increase the trivialness of a map is said to "trivialize" that map. A mechanic which preserve trivialness is described as "balanced".
In this way, Divine Pulse without RNG rerolling is "balanced" because it affects neither the solution space nor the strategy space. RNG rerolling trivializes maps by making weak solutions stronger (it could go either way, but it is hard to imagine anybody use RNG rerolling to make a fail strategy even more guaranteed to fail). Any mechanics that only benefits player, or lopsidedly benefits the player trivializes map by introducing more solutions than deadend.
Why would there be any such incentives? Imagine your armor knight has an exact amount of defense, such that axemen deal exactly the same amount of damage with doubling and combat art, and the axemen choose to double. If your armor knight gets one more point of def, then doubling deals two less damage and combat art one less, and the axemen now choose to use combat art, since it would deal one more damage than doubling, but the combat art in the second case still deal one damage less than doubling in the first case, so overall that one point of def has saved your unit one point of HP. To summarize, even though the enemy switch to a different mode of attack to deal more damage, the final damage your unit takes is still reduced by the def you gain, so more def is always better. The only difference is that, beyond a certain point, every new point of def start to worth a bit less, but its net worth is still positive, and because def is a snowballing stat, the higher your def the more each point is worth, I think this is a bonus point, not minus, since it also solves this problem. The same thing applies to dodgetanks.
The only problem is when the combat arts inflict additional adverse effect, like Encloser and gambits. One need not concern oneself with gambits, since they always deal less damage than combat arts, for their individual might are often lower than the might of silver weapon, and their hit rate is 80 max, so likely lower than combat arts (Even if right now some gambits have more might than silver weapon, 1) they would still deal less damage than combat arts and 2) we can just decrease their might, since the reason to use them is rarely for damage). The only instance where gambits deal more damage than combat art is if your unit has very low charm, like 12 points lower than the enemy. But then, isn't that the whole point of the charm stat? That characters with lower charm gets hit by gambit in exchange for higher stat in other areas? This is also why I propose Fusilade and not anything else, since otherwise enemy will not ever choose gambit over combat art. So onto combat arts, the only relevant combat arts that do things other than damage are bow combat arts, in this case Encloser. Solution is 1) increase enemy archers' speed and 2) weigh your character down when you do not want to get hit by it. The first step has other justification also: it ensures archers can actually kill your fliers. The second step is not perverse at all, since: 1) intentionally weighing your character down to avoid killing an enemy has always been a staple tactics in Fire Emblem, and this is no different; 2) if your character is somehow so fast and strong that no weapon in the game can possibly weigh them down enough so that enemies can double them, you have other bigger problems to worry about. Maybe this will give players some reasons to use steel weapons over silver weapons?
It won't, for enemies are almost guaranteed to use combat art instead of gambit, unless your charm is very low. And by balancing stats, I mean something along the line of low charm but high strength high def and such.
I do not have a definitive solution to this, so if anybody has better solution, I am eager to listen.