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So being as energy efficient as possible before deploying Beacons seems like a really good idea.
Using max productivity modules is the best and only way to get resources from energy. The first beacon add 0.625 to the 0.5 speed of the asembler, which is a must since that more than doubles its speed. The second beacon is also almost a must since that increases the speed from 1.125 to 1.75 or by 56%. Pretty massive too.
It is not a good idea to use energy efficiency before beacons because then when you move over to using productivity modules you'll get a huge increase in energy need all at once. Better to slowly get used to higher need.
If you are already late-game and have an abundance of energy at your disposal, then by all means use Speed Modules in Beacons and Productivity Modules in your resource structures. But unless you have a couple of Nuclear Reactors generating power that you can spare, I would advise caution. Each of those Beacons consume 480 kW on their own, without the Modules. Double that with the Speed Module 3s.
You do not really get free resources using energy using a Productivity Module UNLESS you offset those disadvantages. By itself one Productivity Module 3 will result in a net loss of 6.5% due to productivity being slowed by 15%. The 10% gain in productivity does not fully offset the delayed productivity. Then add to that an 80% increase in energy and a 10% increase in pollution. Productivity Modules should not be used at all, unless you can offset those disadvantages to a large degree.
So just place down twice as many assemblers - again, a one off setup cost. Infinity > any finite setup cost.
With four Productivity Module 3s you are delaying productivity by 60%. Which means that for a normal assember to produce 100 units in a given time period, it now only produces 40. However, it now has an increase of 40% in productivity, resulting in 16 additional units in that given time period. So now you are producing 56 units in the same space of time that it took you to produce 100 units, only now you've increased the pollution of that assembler by 40% and increased the cost in energy by 320%. Where exactly is the advantage again?
With Speed Module 3s in Beacons that surround your assemblers it can mitigate, or even completely offset that 60% delay caused by using four Productivity Module 3s. Only then can you actually get resources by expending energy.
Without beacons I wouldn't use 4 productivity modules simply because the cost in modules is so high and every doubling of the number of assemblers means you need to double the modules too. That's where the price is. In the modules themselves. It's not in the assemblers, not the infrastructure (whether robot or belts), and not even in the power. If you are just concerned about increasing production you should not place modules in the assemblers, just leave them empty and build more. The only hindrance to this is logistics since the blueprint gets very large very quickly with no modules.
You want to reach max allowed prod3 modules per production building. At first because it is resources from energy, but later also because productivity adds multiplicative to speed, making them not even produce much slower than putting in 4 extra speed modules instead (88% with 8 beacons). However at first having 4 prod3 modules is prohibitively expensive in anything but the very most expensive recipes, like for the rocket parts and science labs. With only 1 beacon hitting 8 assemblers you cut the total number of modules required to do the same job from 72 modules down to 32. That's the main purpose of beacons imo (at least in the mid game), to cut down the total number of modules required to do the same job.
I agree with your assessment of the purpose of Beacons. They are to offset the disadvantages of using other Module 3s in assemblers - particularly Productivity Module 3s. With lots of Beacons (using Speed Module 3s of course) you can significantly increase productivity, but at a cost in the form of energy.
You were pretty much saying that if something cost 15% or even 50% speed for 10% productivity then it is not worth it because 50>10. That's what I objected to, because that 50% speed is worth less than 10% productivity. ie it is much easier to just build more assemblers than it is sourcing more ore fields. And also when increasing productivity of a high-end product, such as blue chips, you may need more blue chip assemblers to keep items/minute the same, but since you have increased productivity you need fewer assemblers all the way down the line. Fewer green, fewer red and even fewer refineries. That well compensates even for the small cost of the extra assemblers required fro the blue chips.
If you offset that delay with Speed Module 3s, then you can actually get some advantage in productivity, but only by using Speed Modules. If you use Efficiency Modules you will still have that delay in production, but it will just cost you less energy. So Speed Modules in Beacons are absolutely essential if you are going to offset the delay in productivity caused by Productivity Modules, not adding more assemblers.
As you pointed out, with 8 Beacons you can increase the speed by 88%, which would not only completely offset the 60% delay the Productivity Module 3s gave you, it would increase your speed by an additional 22%, and increase your productivity by 40%. Granted, you are now paying (480 kW x 8 x 3.5) 13.44 Mega Watts for those 8 Beacons with Speed Module 3s, and you are also producing 40% more pollution, but at least you are getting more resources by only expending energy. Woohoo!
Productivity modules stack multiplicatively, unlike the other two types which stack additively. If I have a production chain like green circuits -> red circuits -> blue circuits, and in every step I save up 40% of production materials, then in the next level I save 1.4 times 1.4 of materials and so on. When you combine this with speed beacons, you end up saving energy because you need to run less machines to produce the raw materials, and less machines to produce the same amount of stuff. Saving materials also saves up on the machines needed to produce them.