What are the drawbacks of the Assassin's katana?

The Assassin's Katana only has 2 drawbacks:

• Unique. If you lose it, it stays lost.

• Not Upgradable. You can't improve it further (like you can other weapons)

Other than that, go have a blast with 5 armour penetration, 100% hit chance and incredibly high damage. No (mathematical) drawbacks, other than what was already mentioned.

There is however the case where you can become too "trigger" happy and become careless, resulting in the death of the soldier and subsequent loss of the weapon. A ranger can solo The Lost missions by wielding it.

Edit:

Opting to go for this weapon also means you're opting to give up on the chance of causing a stun with the Arc Blade or the burn effect with Fusion Blade, but that isn't necessarily a drawback of the weapon, but instead a choice of the Commander depending on what's more useful to the squad.

Yep, all the Chosen drop OP weapons. This gives you (another) incentive to kill them all before tackling the final mission.

The only drawback is that, as you mentioned, they're unique, so if a soldier dies with them (and you don't recover their body) you lose the weapon forever.