There is also the matter of the Crests, Gambits/Battalions, and Combat Arts.
In Three Houses, Combat Arts are powerful skills that use up an amount of a weapon's durability in order to deliver strong attacks. These Combat Arts can vary in their effects; for example, one combat art, Smash, simply deals more damage than a regular attack, while another, Monster Piercer, is a specialized attack that deals more damage when used on a monster unit. Having Edelgard use her axe, Aymr, gives her access to the combat art Raging Storm, an attack that is deadly to dragons and gives the character a free turn (ala Galeforce) if it lands. Implementing Aymr's effect in Smash would be something like there being a chance from RNG to make the end lag of one of Edelgard's attacks be significantly shorter than usual and leaving her to do additional options.
For Gambits and Battalions: Battalions are armies of mooks that surround a character on a map. This was implemented by one of 3H's game directors as he felt that it was becoming more difficult to demonstrate war with just one-v-one battles in past Fire Emblem games in this gaming generation. But these Battalions are not for show though, they are instrumental for a character to execute Gambits, AOE attacks that are critical to weakening monsters and incapacitating enemy soldiers and units.
These Gambits can vary in the size of their AOE; one might just affect two spaces in front the character, while another might be a massive amount of spaces in front of the character. Using some gambits might also have different effects; one might switch the positions of the character and the enemy unit that it was executed on, one might push an enemy back, and so forth. Either way, Gambits incapacitate units that are affected, leaving them unable to move for one turn. Something like a shield break or sleep status effect, except you can't button mash your way out of it would be very interesting to see.
Oh yeah, I almost forget, some Combat Arts have AOE damage like Gambits.
Crests are blessings that grant different powers and properties to characters and are triggered randomly by RNG. One crest can heal a unit if an attack lands, another raises the damage of the attack, another can randomly no-sell an enemy attack. Without diving into spoilers, the power of Crests give Edelgard the ability to randomly deal more damage than usual, shut down enemy counterattacks, and/or heal if an attack lands. How would crests work in Smash? Think Command Selection with Psyche Up, Kaclang (minus the metal effect and stillness), and Heal, except you have no control over when it happens and what effect it chooses. Don't forget the random crits that come along with it.
With Hero bringing along RNG, I personally find that there is no excuse now for a Fire Emblem character to not bring along RNG. Crests can justify Edelgard having RNG and the gameplay mechanics of Three Houses implemented into Edelgard can allow for a fresher, more exciting character than the current FE cast if implemented in the right way.
Personally, my implementation of Edelgard sees her using a twist on Robin's durability mechanic as well as Joker's Rebellion gauge, except her specials and attack animations change based on the axe she wields. When she has a regular axe, her attacks and specials are standard. But when she pulls out Aymr, her specials change to Combat Arts which deal more damage and have different animations, and she becomes a much more dangerous fighter as a result. She also has her Crest mechanic, which either randomly boosts her attack power, randomly negates an enemy attack regardless of strength, or randomly heals her if an attack lands. Unlike Hero's crits, Edelgard's crest mechanic applies to all her attacks, not just smash attacks. Thought Hero's smash attacks were "fair and balanced"? Wait until you see all of Edelgard's attacks have RNG attached to them. My final Smash would either be a Combat Art, or a Gambit. Don't know which one to pick. Oh, and if she has Aymr out, there is a chance her end lag is significantly short after throwing out an attack.
She's 5'2. By Smash standards, her short stature would stand out a lot; she's shorter than Little Mac in Smash! Even if they rescale her proportions, she would probably a head shorter than Marth/Lucina!