You completely underestimate the chaos of melee fights. After the focus of the battle has passed sure you could find a wounded noble, assuming that your side held the field and scored the victory. The wounded soldiers could just as easily be walking wounded as seriously wounded requiring aid to leave the field.
Think of it this way, you can scavenge the battlefield if you lose, why do you expect you could wonder around it looking for nobles whom mostly likely would be captured by the enemy that control the field anyway.
I'm not underestimating it so much as disregarding it completely. A nobleman stands out, simply put, from the rank and file of his hirelings. It's like comparing the destruction of a main battle tank to the death of an infantryman. And as each knight or lord brings an entourage of scribes, lesser nobles, advisers and yes-men with them, there are plenty of eyes that are only watching what happens to their patron, and could easily report what happened to them to the army at large. You do get a message when someone is captured, or wounded, or killed in the battle; this request is more about doing something with that rather than introducing new ideas.
You don't get to pick through the gear of the fallen but you
do get to collect your wounded. A wounded nobleman would be easy to spot, just look for the sun shining off his platemail. As for assuming that any missing noblemen were captured by the enemy, typically the enemy would send word of any captures, whether to illicit a ransom or simply to flaunt it. A nobleman is not just another soldier, they're an invaluable instrument of the realm. They are part of an intricate distribution of power that trickles down from on high and are not to be disregarded as the average footman may be.
