I believe the tanks are so strong because the devs balanced them around their position in the tech tree.
Not to be curt towards FXS but the balancing (which in terms of

/

is unchanged since vanilla) was not that deep. If it was they wouldn't have made pikes cost more than knights on release, for example.
At a global level, tanks are not even anomalously strong.
The progression of unit strengths per era is 25+10 per era after ancient. This would mean we would expect something like this:
Ancient era-25
Classical-35
Medieval-45
Renaissance-55
Industrial 65
Modern 75
Atomic/Info 85. The last two eras are functionally one on the unit upgrade tree.
Further, for an era strength of X, ranged units have the stats X-5

/X-15

. Units that can be built on turn 1 have -5

(warrior, slinger.) The archer is a special case, presumably because it needs to fight in the classical.
Anyways, let's look at the melee line and fill in some UUs to the gaps:
Warrior - 20 (reduced 5

because it's a turn 1 unit)
Sword -36
Khevsur etc - 45
Musket - 55
Redcoat/Gardes Imperiales -65
Infantry -
70
Mech Inf - 85.
Infantry and AT crews for whatever reason are at 70 instead of 75. They are unusually weak and this contributes to the tank thing.
If we look at heavy cav through the ages, they follow the trend with a +3 and +5

boost. Chariots, Knights, Tanks, Modern Armor are 28/48/80/90. So tanks are quite consistent with other heavy cav throught he ages; it's the other units that have the bottom fall out under them. Whoever designed this +10 scheme did a good job.
Because of unit gaps being so big at release, they probably adjusted some stuff to give us the odd balls. Yet many RF UUs fit the plan- malon raiders are a 55 ren unit. The domrey happens to fir perfectly between catapults and bombards if you used a +10 per era scheme Pike and Shot are very curious because they exactly fit the mold, even though pikes themselves don't. Of course, eventually the unit gap issue carried over into the units they made to plug it: Cuirassiers are 64, which so happens to fall numerically halfway between knights (48) and tanks (80). Which is nice, and works well enough because the industrial era only has 2 other land units. But again: why did they make redcoats 65, a +10 upgrade over muskets, consistent with almost everything in the game, if they had always planned infantry to be 70? But then inexplicably made mech inf 85? Why are field cannons at 60

/50

if industrial units weren't supposed to be 65

? They have never done a cost or strength rebalance in a comprehensive way. They changed the unique melee units on military tactics, then they added some stuff in GS and later tweaked air units. Costs previously (and for most units to today) were almost strictly governed by where they unlocked in the tech tree on a left/right basis. Buildings were the same way, which is why they touched up some of it with GS' power system.
TL;DR it was almost certainly not part of the design to make the tank unit, and only the tank unit (modern armor doesn't have this same advantage) +10

vs its peers, or in other words,
+50
%. In Civ5, this would be like if they had infantry at 70

, and tanks at 105

- stronger than civ5 modern armor!