This is a big question, so I can only really answer in generalities. Still, I'll do what I can.

Or is the "fight to the death" mentality not really true.

Armies are big, expensive things, to say nothing of the human cost of combat. To fully commit to attacking or defending a place means that the outcome of that battle must be absolutely decisive - something that will win the war. Such instances are pretty rare. What one battle could an army win to conquer the Frankish Empire? Or subdue the thirteen rebelling American colonies? Without the ability to win a clear decision, it's often better to keep the army together and wait for a better opportunity. In instances where one side does commit to a position - Thermopylae, the Alamo, Verdun- casualties can be extreme.

Also, remember that, in Western history at least, a lot of the more famous conventional military campaigns have been pretty symmetrical; both sides have similar weapons and capabilities. In most melee battles, the winner will take almost as many casualties as the loser (barring something weird, like Cannae) until the losing side breaks, runs, and is cut down in pursuit. During the age of muzzleloaders, professional military units engaging in an open-field shootout would both send about three rounds per minute into the enemy formation, resulting in similar casualties no matter how many people were involved.

For a discussion on the difficulties of achieving a decisive battle, check out Russ Wiegley, The Age of Battles.

In addition to /u/TRB1783's comment it's worth noting that for many periods of history we just don't have very reliable figures for the size of the armies involved, and modern estimates are often distinctly different from contemporary or near-contemporary accounts. So if you look at something like the battle of Yarmouk, most modern historians estimate that the Byzantines had something like 100,000 troops in the field, while Tabari, writing a couple centuries after the event, says the Romans had 200,000 men, of which 120,000 were killed, so the numbers are really all over the place.

As a result, we might be able to say with some accuracy that a battle took place on a given date at a given location, but very little about who was there and what exactly took place. I'll let others speak about their own fields but this is very much the case with the Middle East/Islamic studies anyways.

edit: Also, a good discussion of your specific question that lends itself to the previous answer is The Concept of "Decisive Battles" in World History by YN Harari in the Journal of World History. Basically the idea is that the historical focus on such battles seems to be out of proportion to their actual impact or their frequency in comparison with, say, sieges or other forms of combat, mostly for the reasons that /u/TRB1783 mentioned.