As far as I understand pop is both related to role and power.
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It's only related to power. Or ideally it should be at least.
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Imo it is both. A TD which is a specialized unit and counter tanks should lower pop than main battle tank that can be both AI and AT, but we are drifting of topic a bit.
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Population is there to "budget" which units you can fit into your army. That's the only purpose. That's why all heavies cost around the same map regardless of role and the PWerfer costs as much as a P4 despite having completely different roles.
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(I took the liberty of copying Hannibals posts in seperate thread since I find this a rather interesting topic. I hope he does not mind.)
Imo the Pop serves more roles than just "which units you can fit into your army" and Pop for unit is not simply related to power.
Pop not only limits the power number of unit one can field but also increases the upkeep of one's army. In sense it forces you make good use of these.
When comparing units that do pretty much the same thing (and not so much have the same role) the power of each unit is directly related with Pop.
When it comes to specialized units or of force multiplier unit the pop is adjusted accordingly.
For instance a TD has lower pop than tank although its gun is superior in AT than tanks. Or certain artillery unit has high pop so that they will not get spammed and abused. Some goes for emplacements.
In sort imo pop can be used for a number of reason including balancing unit and preventing spamming. That imo was the case with Churchill who although not extremely powerful become an issue once produced in numbers. Thus is got one of the highest pop for stock units although not reflect in its price/power. (Actually it could see a small reduction in pop 1-2).