Size of house militaries...
We have the exact strength of the LC army 122 regiments, uncertain if this includes the 17 mercenary regiments since the Tamar Tigers were listed and they were officially mercenaries. IMPO those 122 regiments do not include mercenary units so the LCAF combined strength should be about 140 regiments.
We have a fairly accurate estimate of the entire DC army size as < 150 regiments, of which some 17 are mercenary units.
The FS managed to raise a 50 regiment invasion force mearly with the units they managed to pry loose from their peacetime bases, IMPO strongly suggesting an available force over 150 regiments with only about 14 mercenary regiments among them. A big but troubled army.
There are no hard facts on the CC and FWL military, however I would rate the FWL about equal, but not quite, to the LC and the CC lower, perhaps 110 regiments total. Also the FWL have a only about 10 mercenary regiments compared to the CC 19 making the CC house army significantly smaller than the other houses, while the CC figure might seem low they did have enormous problems just halting a 10 regiment drive despite the FS being mostly inactive on it's other front.
I think a edict of 2650 limit of around 40 regiments seems a good balance. When it was revoked the houses built up to about double that and later in the race the CC fell a bit behind while the industrial giants of the FWL and LC bulked up better. The FS and DC might not have the industry of those two but they have been cheating for much longer.