Has anyone done a production analysis to see if there really is more production cost to the higher tier goods?
Yes, it's about space needed to produce the goods.
For example once you include the culture, roads, supplies, and the population that it requires.
Your level 23 marble factory takes up 75.6 squares
Therefore your level 23 marble factory makes 143 marble per square
Your level 19 Crystal factory takes up 75.6 squares
Therefore your level 19 crystal factory makes 104 crystal per square
Your level 19 Gem factory takes up 75.6 squares
Therefore your level 19 Gem factory makes 56.6 Gems per square
So you are able to make
2.5x the marble in the same space as gems. Not 16x.
1.9x the crystal in the same space as gems. Not 4x
1.4x the marble in the same space as crystal. not 4x
We ran a few scenarios about a year ago, and the 5:2:1 ratio was close in most cases, but it does fluctuate a little because you rarely have all tiers of factories at the same level. Your specific ratio is close to 5:4:3 Also, the demand for all tiers of goods is not equal in all chapters e.g. tier 3 has no value in chapters 1&2.
All this makes it very hard to determine a fair exchange rate for cross-tier trades, so many players just avoid/ban them
You can see the "true" size of production buildings here
https://us.forum.elvenar.com/index.php?threads/elvenar-efficiency-calculator.17073/
I used 9h+3h+9h productions for the above example, but it doesn't make a huge difference if you change it to 9h +3+3+3+3+3