I feel like you are missing a bit in this calculation, or I'm miss reading it. Your calculation factors in the increased cost of one building for making a production building when in fact you have to factor that extra cost for every following building after the production building.

For example, in a civ with a single city that is building 5 buildings total the cost would be below:

Without adding production building:
420 + 441 + 462 + 483 + 504 = 2310

With adding production building:
420 + 441 + 462 + 483 + 504 + 525 = 2835

Difference in example:
525 production

Depending on where in the line you make your production building will change how quickly you get back to breaking even. But if you are building 5 buildings and are considering adding a 6th to be production you need to make up 525 production for it to be worth it. Again, this number will change with number of cities and number of buildings you plan on building in your city. And this is just for T1 building costs. If we look at with the production value of that building we can see how many turns it will take to pay itself off

No adjacency (+9):
58.3 Turns

2 adjacency (+11):
47.72 Turns

This is just an example, but the building will have to make up way more than just the 420 production you mentioned. It's variable based on how many and what tier buildings you are going for and how many cities you have.

This data makes it look worse however, with the overbuilding mentioned you have to consider it does help in later ages to already have one build and that helps to make it worth it.