I don't feel like it will make each playthrough unique if players are allowed to choose because most people will choose the same thing each time. If you want it to be truly "unique" each time, it should happen organically and be chosen at random, allowing the skill specializations to influence how the player chooses to use them, not the other way around.
Personally I don't like to use grenades, so I would never choose the grenade specialization on my own. But if I happened to recruit a soldier who's specialization was grenades, I would make the smart choice and give that soldier grenades to make best use of their skills. It would help me experience the game in a way that I was not previously experiencing it, because now I have to think about combat differently to incorporate grenades. I've also literally never used a Deadfall trap or an IED, so I would be even less inclined to pick any skill involving those. (I'm actually about to try to use those, because I feel like I'm missing an aspect of the game)
To be clear, I still think this is a great idea, I just feel most people have a very one-track mind when it comes to the way they play the game, myself included to be honest, so allowing them to choose will ensure that they only ever play the game in the same way each time.
BUT it's a great idea no matter which way it's implimented
Personally I don't like to use grenades, so I would never choose the grenade specialization on my own. But if I happened to recruit a soldier who's specialization was grenades, I would make the smart choice and give that soldier grenades to make best use of their skills. It would help me experience the game in a way that I was not previously experiencing it, because now I have to think about combat differently to incorporate grenades. I've also literally never used a Deadfall trap or an IED, so I would be even less inclined to pick any skill involving those. (I'm actually about to try to use those, because I feel like I'm missing an aspect of the game)
To be clear, I still think this is a great idea, I just feel most people have a very one-track mind when it comes to the way they play the game, myself included to be honest, so allowing them to choose will ensure that they only ever play the game in the same way each time.
BUT it's a great idea no matter which way it's implimented