I bought GC3 a few weeks ago. I've through the campaign and several custom galaxies and every time the same pattern emerges. It is very very easy to generate enough manufacturing to produce 1 improvement/turn. With a full transport, the "Prolific" trait, and just a government tech or two, a completely fresh planet can produce 1 basic improvement/turn from the very first turn its settled. Even without those things the first 1-2 basic factories will take 2 turns, and everything after takes 1. The 1 improvement/turn limit turns into a bottleneck whereupon you either micromanage the production palette of each planet that built a new factory each turn, or you end up with an escalatingly inefficient remainder of hammers that will be completely wasted until you finally get to sufficiently expensive improvments.
On dedicated manufacturing worlds, that will never happen. With the proper mixture of factories and farms, they can easily produce enough hammers to make any age of war improvement and a very fancy constructor every turn, and still have a massive amount of hammers going to waste. These worlds will only ever make use of their full power when building capital ships that I purposefully make as expensive as possible. These planets would build 5+ constructors in a single turn if they could, and you might think, who needs that many? But on a large enough map you can and should have 40+ mining starbases, meaning you need to build 40+ new constructors to make the most use out of every new mining tech. The reality is that you will have enough hammers to build a fully functional eco starbase for every single planet you own, but 1 constructor per shipyard per turn is simply too slow to keep up with the hammers you have available or with the number of starbase modules that you actually could make use of.
Even on 75+% research worlds, it is so easy to generate 30-45 hammers that once again, the development of those planets is only bottlenecked by the 1 improvement/turn limit when building tier 1/2 improvements.
And once you have enough of those planets finally taking 2-3 turns to build level 3+ research improvments, your empire will be producing enough beakers to research anything in the age of war in 1 turn (the more expensive ones that theoretically should take 2-3 turns actually only take 1 because of the buffer you build up over-researching the earlier techs). In the game I'm playing right now, I have 77/100 techs needed to advance to the next age. I can tell that I am exactly 23 turns away from reaching that age, because I have researched everything in 1 turn for quite some time now. If I could research more than 1 tech/turn I would probably advance the age in <10.
Since everything can be built in 1 turn and purchasing something actually puts the associated production queue on hold for that turn, BCs are useless for anything other than maintenance and invasions.
This situation simply does seem to be healthy or intended. An empire should be bottlenecked by its total output, but right now by turn ~50 a well managed empire will progress by 1 improvement per planet per turn, 1 constructor per shipyard per turn, and 1 technology per turn.
Possible fixes:
1. Allow planets to sponsor more than 1 shipyard. As previously covered, a full-power manu world could probably power 5+ shipyards in 99% of situations.
2. Increase the cost of everything in the age of war by 5x or more so that your hammers actually have something to do.
3. Remove the 1 per turn limit on everything so that your overflow hammers are made proper use of.
4. Fix the rush-buy / production halt bug.
5. Make planets sponsor starbases to build modules, instead of requiring infinite constructor spam.