It seems to me that on simple inspection, the different levels of units are pretty much the same regarding the cost vs. strength, so that purchasing 600 heavy spears is pretty much the same as having 1000 light spears. The main advantage, as has already been stated earlier in this thread, is that heavies use up less population. However, for people with high pop. growth this may not be a big issue.
No. Moral is much more serious than population loss.
There are several reasons for light troops. One is that light troops carry more resources. Several posts already mentioned that. Faster movement can also be useful for taking resources, especially from gold mines.
More relevant is the cost of research. Setting up a battle between 1200 heavy cavalry and 2000 light cavalry does not reflect the cost of research. I have not calculated how many light cavalry you can deploy for the same networth as heavy cavalry. For paladins it is about 20,000 paladins. What I mean is that a player can have 40,000 heavy cavalry with mellee 7, armor 8 and have equal networth with a player that has mellee 14 and armor 14. (version 4a). So the battle comparison is 80,000 heavy cavalry against 20,000 paladins.
A third factor is flank cavalry. Compare in the plains with melee 14 armor 15:
10,000 paladins with 40,000 lite spears vs 12,500 paladins.
loses 1450 vs 9350 moral 68
10,000 paladins with 12,500 phalanx vs 12,500 paladins.
loses 1650 vs 9350 moral 84
I have also noticed that lite spears tend to inspire people to pull elite archers out of the fort and send them along with attacks. In combat rounds 5,6 and sometimes 7 the attacker still has guardians and a few elite archers. Many of the light spears disappear in rounds 1 and 2. In round 5 the attacker loses moral because (s)he is fighting pure flank cavalry. This most effective in the forested mountains with high fortification research.
20,000 paladins, 30,000 guardians, 10,000 elite archers vs 10,000 paladins, 40,000 lite spears in forested mountains.
Calc says a moral loss of 36 before the fortress battle begins. Against a boxed fortress with archers in the fort the attack is likely to fail. Of course you still lose your army but I think it is great fun anyway.
Honor is a fourth reason I feed light troops into an elite army. If you are send 20,000 paladins with 400 catapults and lose 800 paladins you get 0 points of honor. Add 1000 light spears your losses increase to 1200 or 1300 troops. That brings you 3 points of honor. A lot of players do not care about honor. The moral bonuses are nice and there is a honor chart. You should try to be on at least one of the charts.