I wouldn't have minded if they would be tied to Grey Worm as commander, bit like the King's Guard is tied to Joffrey when he steps on the battlefield...but i find it odd to believe that all Unsullied troops with swords behave like that, whatever the price.
What makes the unsullied so great is their discipline...so i can definitely understand a resistance to condition and having a tremendous morale. What i can't understand is how much destruction they can do...10 dice at 2+ with precision will create more casualties than many cavalry charges...which makes no sense at all considering the sacrifice that those lance units pay for. Besides, they were described as being physically less potent than fully grown men (being eunuqs).
If you look at Flayed Men's new and improved card(sic)...and this (both costing 9pts), it makes 0 sense, and before people say "play them first"...we've been played long enough to have an idea of what those stats mean on the table.
I'm not quite sure comparing them to Flayed Men is fair, as Flayed Men are a neutral unit and cavalry to boot. They're going to pay more for the flexibility of an extra maneuver before their attack. On top of that, cross-faction comparison usually doesn't yield much in the way of insight to how a unit performs unless you look broad category to broad category (e.g. assault unit to assault unit, elite infantry to elite infantry).
So, sticking with the category of super infantry/elite infantry - here's the Unsullied's competition, and most fair comparisons:
Stag Knights. No questions here, they are vastly superior to Stag Knights - most 6/7 point units are, and Stag Knights have been beaten to death with the same stick over and over. No need for further analysis.
Warrior Sons. So for 1 less point, you have same armor and morale stats and 1 less movement. Faith tokens are finnicky, and require some planning but they 1) get tougher as they die and 2) can dish out serious damage with their faith tokens situationally, before accounting for the wound restoration and other Lannister tricks that can make this unit a thorn to remove. It's also worth noting that this unit exists in a faction with 2 rather solid cheap activations with staying power in the form of Guardsmen and Poor Fellows, which Targaryens do not necessarily have in spades.
Night's Watch Veterans. For 1 less point, 1 better armor save, 1 worse morale, and a pretty solid attack profile like Warrior Sons. Obviously cannot compete with 10 dice on 2s with Precision, but Veterans have the ability to get situationally powerful benefits from Vows (which can also last the whole game if needed) and counterattack makes the unit rather nasty as well, with the ability to essentially sustain themselves through the whole game with Jon and/or Maester Aemon. They also exist in a faction with cheap, durable activations and one of the best standard mainline infantry in the game - Sworn Brothers (perhaps less so after the point increase).
Starks might not have a direct parallel, since their infantry units all come in 7 points or under but Greataxes seem the most appropriate. 2 points cheaper, ability to ignore armor saves, and lots of mobility tricks as well as a faction with the ability to drop lots of things on the board and cover lots of ground (wolves, crannogs, and sworn swords all rather cheap).
Free Folk no real equivalent except Bonelord's Chosen, but that starts to get dicey with the rest of Free Folk and the fact that the commander is attached, or Rattleshirt is in there somewhere.
All this to say that faction context is important. Yes, they do a fair number of wounds, charge or otherwise. Yes, they have the ability to activate several times. But they're still 1 unit, and again, that matters. They cannot be everywhere, and they're not cavalry so though they are rather fast at 6" or 7" of movement (pending Dany), their mobility is still rather limited and you can cancel a lot of their multi-activation stuff by smart use of retreating, just like you might to avoid and work around giants. In the context of Targaryens, a 9-12 point unit is an expensive decision to make, and if you catch the Unsullied off-guard and do not let them charge you, a lot of their oomph can be mitigated by denying a lot of the nastier Targaryen cards, and unless the Targaryens wipe their target in one swing they're liable to get locked down and die just like any other uber unit. And again, 12 points (because the officer is one of the biggest things that makes them so good) means your combat presence on the board is limited, and the number of NCUs you can take is hampered.
Yes they're a good unit, no one is saying otherwise, but I really don't think they're broken in the context of Targaryens. A 9-12 point infantry unit should perform this well, because it's a 9-12 point infantry unit.