I think the AC v Melee comparison is pretty logical. They're both foot units with a lot of bonuses that apply to both in the realm of attacking walls, oligarchy, etc. AC are supposed to be great cav counters but as is recounted in this thread they aren't very good at that; plus AC don't get to exclusively attack cav, no unit can solely rely on attacking one thing. Since melee really outshine AC in the "everything else" department it's just a logical line of inquiry if you're better off dropping AC.
Again, a tank hits another tank just as hard as an AT crew does and moves twice and fast and hits all other units for +10 over the AT. For a mere 20% more production + 1 oil. Maybe you can't make 20 tanks but in the realm of 4-6 you definitely can.
The cost difference between legions and regular swords is over 20%, for goodness' sake. If we just chalk the +2

movement up to oil, can I have my legion unit lose the builder charge and get 46

instead?
I don't think the current scale of civ6 battles is as conducive to a cost based balancing as it is to strength based balancing. At least for something the devs might actually change. Since we don't currently see a huge P&S or At crew spam, I am quite confident that spears+pikes getting boosted to 30 & 45 respectively would do great things for combat. (Swords still beat pikes for half the price. You might have to actually build pikes in the middle ages! Gasp! the horror!). Extending the same logic to making AT+infantry 75 and Modern AT 85 (at least give these guys some love!) would fully round out the cast.
If it makes medieval cav falter too hard, we can always round their strength to an even 45 & 50 so things are generally consistent through the ages. (I would also love to see 85

helos but I'm drifting...) Hey, the Black Army was 50 strength in the Hungary reveal video. Just saying, there's precedent.
Insofar as cost goes, it is a noble goal and i would love to see a lost of cost rebalancing in the game, but +10

is a
50% attack and defense bonus. So to balance two identical units at X and X+10 strength, the weaker unit needs to be about half the price - because the stronger unit expends 1.5x less HP to kill 1.5x more unit. Total efficiency ~2.25x. If you think it should only be a 1.5x factor, ask yourself: If you could build either a Tank or a Modern Armor, which do you make? A tank costs 480 vs MA's 680, 70% of the price. A 1.5x factor would suggest a 33% cost reduction or about 460

. That's incredibly close - does anyone think Tanks and modern armor are that close in combat?
Similarly, swords vs military tactics UUs like the khevsureti - 90

vs 160

for about +10

. Shouldn't even be in the ballpark, everyone should prefer swords.
Units in general go up 10 strength per era and the cost rises extremely fast for most of the game. Yet we all rush for upgraded units...
I mention this because if you have an equal amount of production split between two armies, one of stronger and one of weaker units, the stronger units will generally win on the field most of the time. They have a lot of advantages in healing, attacking, the fact that civ6 fights don't all occur on an infinite featureless plain, and so on. And then there's stuff like the strong units can kill off a weaker unit faster than the reverse on all but totally open terrain, so the next turn the weaker army has to counterattack with a reduced force.
Anyways, Strength buffs FTW