There are some questions than add to the problem.
1.- Replacement trick (i.e. replacement costs perhaps half as new unit) adds a few more troops. Luckily an extra division can be raised a year by using it. Not too much in fact but it adds a bit. (125 men on average are free per militia element)
One of the problems in my opinion is there are TOO much FREE MILITIA replacements during the early months.
2.- Maxing too much the Volunteers / Mobilization / National Morale bonus can add a lot of divisions.
A full mobilization adds around 5 or 6 divisions a year...
And the difference betwen a minimum free volunteer and a 3k pay can be 4 extra divisions a year!
(I ve never been able to pay so much for them, but some time I ll do

)
This can be the most important problem, too much extra units can be raised this way. If you want to down the total division CAP, those figures should be a bit/lot downgraded, instead of limiting the DIV total.
3.- Many USA players dont assault enemy troops, in fact, a lot of times they just advance into void terrain or are extremely cautious, so no battles are done and troops dont die as fast as in the real war.
This is not a problem for me, if few battles, few Kia, so upper limits for little battles is ok. But CSA still gets too low commandments for leading them.
EDIT:
4.- No Attrition of course!
If we want to play no attrition, then surely in the long run a lot more units could be in the field. How many men were lost to attrition ? Dont know...180.000 in the CSA?? This is 18 divisions!