Cheap, light, warm.

You only get two. Never all three. And light usually also means less bulk.

Down will always be lighter and more compact than a same-rated equivalent synthetic bag.

You're right that most bags are not rated accurately. Some are - Western Mountaineering for one. Marmot has EN rated bags, so if you read the EN rating you see that the comfort rating is different for men than for women, and that the stated rating is often not the actual rating - but they tell you that. My 0 degree Never Winter bag cost me around $130 on a closeout at Sierra Trading Post, but the EN rating says that it is actually a 17F bag - and that is accurate for me, because I had it down to 15F and was fine.