Wait Mode skill tree appeals to a Tactician whereas Active Mode appeals to a Strategist and the benefit of spending AP in WAIT MODE is great should you find more comfort in a tactical role.
The AP in wait mode is designed to give players the same scope of information afforded in Active Mode, standing still.
For example, on PS4 Libra is activated with R1 (RB in XBOX), but you have to select the target and you typically only have a brief moment you can check Libra during combat. In WAIT MODE, you can be more precise in your actions because you have time to plan while you do not move.
As long as you don't plan on playing in Wait Mode, you're fine without using AP in the skills. If you do plan on it at some point however, Wait Mode is weakened unless you use the AP. Fortunately, the AP required is minimal compared to other skill trees.
For combat differences:
According to the Wikia, Easy Mode will make enemies weaker and have Carbuncle prevent you from dying numerous times before you actually die.
Final Fantasy XV also has a standard difficulty and easy mode. The player can change difficulty at any time. The easy mode is made so that one can generally win by just button mashing. In the easy mode, Carbuncle can appear to heal Noctis if he is in danger of dying.
Note that you can still die on Easy mode. See this thread:
Many will tell you it's impossible to die in easy mode but that simply is not true. It's tougher due to Carbuncle reviving you a ton of times, but i've tested this, and you can still die in easy mode because he will stop reviving you eventually.
I went up against an Iron Giant on easy and still died after only being revived a good 3-5 times. After that, Carbuncle just stopped showing up which led to a game over.
Lastly, it appears that you can extend the amount of time you can spend in Wait Mode if you are playing on the Easy difficulty. See here:
If you want to have a longer wait mode, you can always toggle the difficulty settings. To do this, enter the pause menu, select Difficulty, then switch to easy. With a lower difficulty setting, enemies are weaker and the wait mode is extended, giving you a longer time to rehash your decisions.
As for trophies, there is a single missable trophy if you play on Easy Mode. From this list:
Chosen King: Defeated Ifrit on Normal difficulty.
Though, I've read that you can switch the difficulty to Normal just before the fight and still get the trophy.
Finally, for your question about EXP or items rewarded, I can't find any evidence of the drop rates/amounts being any different across difficulties. From the same thread as earlier:
As far as I know, yes. But I wasn't really counting the EXP when doing my Carbuncle tests on easy.
Best Answer
Aside from boosting your stats exponentially, there are two benefits for using the Royal Arms:
Deals non-specific weapon type damage, which are useful against enemies who have physical resistances. i.e. The Katana of the Warrior functions with mobility and style of a sword, but deals regular damage to enemies who have resistance or weakness to swords.
Enhances Warp Strike, Blitz Combos, and/or Directional Attacks to make them more powerful and effective by giving them additional abilities. iDigitalTimes Royal Arms contains a breakdown of each of the Royal Arm's hidden abilities