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Re command points vs supply. I have a theory
You core infantry is supposed to be in transports, generally infantry in trucks and engineers/heavy infantry in halftracks.
I suspect (some) players prefer to use the 1-LCP saved pr unit by not adding transport to buy an extra unit or two instead.
There may be a game issue where one infantry/infantry in trucks both use 3 supply points. So if you skip trucks for three units and buy another inf unit, there may not be supply left for the extra unit.
That would explain the supply issues you've seen.