How about we stop covering shittness with abilitites and just make it AOE better? Or why AVRE was never nerfed to sturmtiger level?
Well this depends. The AoE data as you presented it in the opening post does not tell you that much in direct comparison since also the damage is very different between the units. If my/MMX's data is correct, then the AoE profiles look like this:

OHK radius:
ST: ~6,47
AVRE:~ 7,18
Most important thing is though that the curves above 80 HP don't matter unless you're shooting at tanks.
So the AVRE has a better performance between 6,5 and 8 meters approximately, but the ST has a huge AoE max value. You can't say that the ST/AVRE is straight out better regarding offensive capability than the other one.
The main difference is casemate/turret, health and armor, so all factors that determine survivability for these units. And since the ST seems to draw the short end of the stick in most regards (especially when looking at its armor and the high pen of Allied TDs), I suggested a survivability buff that also needs micro to use correctly. Frontal Armor might be a second option, but I also think that at least the rear armor of the AVRE should go down to 150 if not even less to allow mediums to pen it better from the side.
Like caliope
There's some truth in this though. In my eyes Calliope could do with 320 HP to make it somewhat more divable. But that's just my opinion