I think one consideration that the forum has struggled with for some time is whether we should consider the trait that we are evaluating in the context of the civ and the game that it is in, or rather evaluate the trait in a vacuum and not account for the compatibility and synergy provided by other attributes of the civ. I've always been an advocate for trying to break down aspects of the game for what they are by themselves and disregard how they are better because of how some other elements of the civ compound additional bonuses that aren't unique to that particular unit/building.etc. As such, I find that some units are given more credit than they are worth, such as the saka HA and the impi, because other bonuses of the civ let you do things with it that aren't specific to that unit. Other units, only one I can think of off the top of my head is the minas geraes, may be underappreciated as while the rest of Brazil's bonuses are fair to good (being quite conservative) they don't add anything to the unit.
Having said that, I now need to completely contradict myself as my comparison of these three units needs to account for the other bonuses of the civs. As
@DWilson points out, it may be a patch or something that I don't have but the production cost of MCA is not 90, which has always been the one and only argument that I've had against it - my sole defining characteristic of the MCA is that it is
prohibitively expensive, Other than that I love it - quick, tanky, and hits hard. It's just that you can't build that many of them and have the option of building 2-3 archers for every MCA, which tends to be a better option at that stage of the game.
But getting back to the context, the other two respective civs each have multiple bonuses that complement the unit so well, and passively not actively, that it becomes necessary to incorporate them. As for the pitati, you mentioned it's cost but didn't account for the civ ability that greatly reduces it; unless some other civ gains access to building that unit the bonus will always be applied and the cost could basically be considered 1/3 less. Also, Nubia's bonus to mines creates additional production and gold, both of which can be used to further increase production. Finally the 20-40% discount to districts means you can re-allocate some of the production from them to more pitati and the districts that you're building combined with the mining bonuses gives Nubia a strong faith- and gold- generation game both of which can supplement production. As for Persia, both the trade route bonuses and the UI give him a strong gold generation game as well, but the key factor is the additional movement for 10 turns, meaning that for a good portion of the blitz they're movement is 4, which moves them from the worst of the three to the best of them. Egypt, however, doesn't have much in the way of other bonuses complementing the unit. I guess you could make the same argument for re-allocation of hammers since districts and wonders are discounted that I made for Nubia, but it's 15% instead of 20% and only applies to river placement - which situationally (although I find frequently) negates the bonus; I'd rather have a campus have mountainside adjacency than a 15% cost discount and often you have to choose between the two. You could also make an argument that the UI helps with faith generation which can supplement production, but that only really picks up if they have world wonder adjacency which implies a very heavy production schedule for Egypt. And as for extra gold for Egypt's trade routes - you can't control other civs sending them to you, and sacrifice production for gold if you're sending externals instead of internals, so I tend to not do that.
But yeah, I'd agree with you that if the MCA had a cost of 90 and evaluating in a complete vacuum of the other aspects of the related civilization, then yeah they'd be the best of the three. Except that in my games 90 isn't the cost and the other bonuses of the civs are so passively incorporated (except perhaps the movement bonus from surprise wars) that the other traits can't really be divorced from being part of the unit.