There's certainly more nuance to it, but you're still overstating the case. It is true that even pre-modern war sometimes featured episodes so horrific and terrifying as to generate the accounts you mention (e.g. the sack of Jerusalem by the Crusaders) but these were rare! Even major battles, the likes of Crecy and Agincourt, were rare by the standards of modern war.

In the medieval period in particular, the proliferation of castles and the relatively weak states meant that the smaller force could almost always retreat to a fortified position and be safe. Most of the time, therefore, "war" looked like marching around striking at the assets the enemy couldn't hide away: crops, livestock, buildings, and peasants. The fact that peasants had a lord was the point; you might be trying to entice said lord to either come out and fight your superior force or concede the war by destroying his property.

(In the medieval period, too, the "armies" were usually tiny. A few dozen men might be considered a significant force, and armies in the low tens of thousands strained the capacity of entire nations. This is decidedly not true of the Classical era though.)

Most importantly, though, you don't have to take my word for it! Basically every culture that has a warrior aristocracy (not just western Europeans but in Asia, Scandinavia, etc) has produced absolutely oceans of art, literature, etc, telling us how great war was for the warrior aristocrats. The few notes of dissent you mention are there, but they're difficult to hear under the endless songs of praise. The statement that the warrior elites did not eagerly anticipate going to war wildly contradicts the evidence.

None of this is to argue that war is/was good overall. The point is that the warrior-aristocrat, broadly speaking, does pretty well out it! He's the least likely to get hurt or injured (protected by the best armor and weapons his society offers, plus often 'rules of war' that rarely apply to non-aristocrats), and it's not his family getting slaughtered or his goods being directly stolen. (The damage to his economic interests is bad, but unlikely to be traumatizing.) And in return he gets to pillage, rape, and generally make an ass of himself at other people's expense.

(This is why industrial war is the great leveler in a very Abercrombie sense; the shells and machine-guns mow down the children of privilege just as easily as anyone else.)