I'm not seeing where your getting any production numbers from. Without knowing attrition rate or even when, or if, a ship is decommissioned we can't determine how often a forge world would need to build a battleship
Production numbers are estimates from canon information, specifically what I noted here:
A shipyard may take several years to construct a Cobra class destroyer, a decade for a cruiser or a battlecruiser and a century for a battleship. A single Forge World may produce one or more cruisers per year as there will always be several in various stages of construction. Smaller worlds may take years to produce an escort, decades to produce a single cruiser or centuries for a battleship.
Battlefleet Gothic notes that Imperial Heavy Cruiser takes between three and 11 years to produce, so "a decade" I noted above is really the upper end of the estimate. Even if we assume that it is 11 years per cruiser per Forge World, and only 2 500 Forge Worlds (which again is basically minimum estimate) we get a minimum of 230 cruisers per year.
This however completely ignores the fact that a) Forge World will be building
multiple cruisers at the same time, b) you don't
need a Forge World to build a cruiser or even a battleship, they are just the
best at it, but a ship may be built even by a Feral World and c) as I noted, "decade" for a cruiser is a high-end estimate.
As for decommissioning, we know that there are still ships serving in the Imperium from before the Horus Heresy. So it seems likely that they don't decommission ships at all... even though we also know that there are
many warships being kept in graveyards, from where they can be quickly recommissioned if needed.
I'm not seeing where your getting any production numbers from. Without knowing attrition rate or even when, or if, a ship is decommissioned we can't determine how often a forge world would need to build a battleship
Production numbers are estimates from canon information, specifically this:
A shipyard may take several years to construct a Cobra class destroyer, a decade for a cruiser or a battlecruiser and a century for a battleship. A single Forge World may produce one or more cruisers per year as there will always be several in various stages of construction. Smaller worlds may take years to produce an escort, decades to produce a single cruiser or centuries for a battleship.
Battlefleet Gothic notes that Imperial Heavy Cruiser takes between three and 11 years to produce, so "a decade" I noted above is really the upper end of the estimate. Even if we assume that it is 11 years per cruiser per Forge World, and only 2 500 Forge Worlds (which again is basically minimum estimate) we get a minimum of 230 cruisers per year.
This however completely ignores the fact that a) Forge World will be building
multiple cruisers at the same time, b)
As for decommissioning, we know that there are still ships serving in the Imperium from before the Horus Heresy. So it seems likely that they don't decommission ships at all... even though we also know that there are
many warships being kept in graveyards, from where they can be quickly recommissioned if needed.
Still being able to make it is one thing, understanding why it does what it does is quite another.
Specifically for this scenario, why would Imperium need to "understand why it does what it does"? It will not make any difference in any timeline less than "centuries". Can the Empire hold out that long? And with Guilliman back, Mechanicum is again innovating.
Well no - in the movies they clearly aren't as stagnant as some of the old EU materials implied.
Maybe. But even so, any major change will take decades.