No they are broken and I will show you how because you meassured the things in a wrong way. If someone asked you what is the main thing that keep the balance between the civs what will you answer him? The answer is clear, it is the counter system. Depending on this answer you will know how Sicilians and other broken civs break the counter system or the counter system barely do vs them. Sicilians have 50% less damage, lets take the knight for example. Since the Siclians knight take less 50% damage, this mean the counter system doesn't work vs them, the Sicilians knight kill camel raider in 1v1 fight with 35hp left, pikes do nothing and you ignored this and kept talking about heavy camels and imp battles and you forgot that actually castle age take the biggest part in the game. But now since camels and pikes do nothing what can I do?! The only thing is mirror, which means the Sicilian player go knights then I will do the same, however what if I have bad stables? The solution is the trash counter or camels? But this doesn't work with Sicilians since their 50% bonus less damage kill the counter play!! Did you realise it now or not?! You are forcing other civs to things they are not good at and make the game go as your civ is and kill the normal counter system. Not only 50% less damage is broken, the 100% castle and tc build is broken too, 1st crusade broekn, etc. By applying how the counter system or normal units should work, you will realise how Lithuans, Burgundians, Huns, Sicilians, Eagles, Mesos, Britons, Wagons, Gurjaras, Hindus and many others are broken.Aztecs is top 5 and Chinese top 10 in the high elo ladder.
And yeah, they get picked often in tournaments, and pros rate them S tier or A tier.
But, which pro rates Sicilians S tier or A tier? If it's as broken as you say it is, surely the pros would pick it more often in tournaments, would rate them highly in their tier system etc. Right?
To use the instant army to full effect, you need 5 TCs and need to happen while enemy is relatively low in army number. Which isn't happening in almost any scenario except in arena or fortress.
And the units that come out of it are mediocre. Almost everyone agrees that sergeants are just plain mediocre.
Not broken. If you disagree, tell me. What percentage of the games do you think were decided by First Crusade? I'll take a wild guess and assume it's less than 5%.
50% bonus damage reduction looks good on paper, but Sicilians otherwise just get cavalier. Sicilians don't get thumb ring, so their arbs also mediocre. Point being, the 50% bonus damage reduction would be OP on a civ which has great units to begin with (say if they had a paladin instead of cavalier)
Sicilian cavalier loses to any paladin, even Byzantine paladin. So, overpowering them with heavy cav is an option. They also lose 1v1 to heavy camels, though they still do much better against them than regular cavalier. They perform nearly the same as a regular paladin against heavy cav archer (a bit worse).
Like I said, their cavaliers are OP only against foot archer civs.