As it happens, we do have a battlefield where over a hundred arrowheads have been found. Work carried out by Tim Sutherland in the late 90s and early 2000s at the site of the Battle of Towton located several hundred arrowheads in an area about 500 meters wide by 180 meters deep. Other finds, such as lead bullets, buckles, buttons and other non-military finds were located over a wide area, extending over a front of about 800 meters, were also found. In another instance, large numbers of arrowheads were found in the early 2000s at the site where the Battle of Shrewsbury was fought.

The issue raised by the Towton archaeology is precisely the one that you mention: if the arrowheads and other artifacts were found at Towton in sufficient quantity to pick out the breadth of individual formations, why haven't the same results been found at other famous medieval sites? Tim Sutherland asked this exact same question after conducting some preliminary surveys at the traditional site of the Battle of Agincourt and turned up some Roman and post-medieval finds, but almost nothing from the middle ages themselves, let alone from the battle. Similar results have been turned up at other medieval battlefields where there is common agreement about the location, such as the Battle of Hastings, and this has led to a number of challenges to existing traditions.

Tim Sutherland has led the charge with Agincourt, suggesting two possible alternate sites - one to the north of the currently accepted location and the other to the south-west - while Michael Livingston has recently come out in support of the position to the south-west. The argument is, in essence, is that the lack of arrowheads and other artifacts strongly indicates that the sources have been misread. Livingston has added concerns about the dimensions of the battle as well, proposing that neither side would have been able to deploy on the traditional site.

The difficulty in the case of Agincourt is that, while there might not be any archaeological evidence, the earliest and - most importantly - most detailed eyewitness account off the battle is completely unambiguous about the movements of the armies up to the battle. The Gesta Henrici Quiniti, written by an anonymous cleric who was present in the rear of the English army during the battle, is quite clear that on the 24th of October both sides faced off across the small valley east of Maisoncelle that runs from Tramecourt to the Ternoise river and that, at dusk, the French moved off towards the English left to camp for the night. As Henry was worried about them going around the wood directly on their left - which could only be the wood of Tramecourt - and flank them, or else continue around a wood further away and come on the English from the rear - which can only have been the woods of Azincourt given the English position at this junction - there can be little doubt that the French were not camped to the west of Maisoncelle. And, given the well attested closeness of the two armies, it's improbable that the French were camped several kilometers north of Maisoncelle at Ruisseauville.

The result is a large disconnect between very clear written sources on the battle and the archaeological evidence that is hard to reconcile. Ferrous artifacts can be very hard to find thanks to a lot of background noise from other non-battle related ferrous artifacts (nails, etc), and they often don't survive as well as non-ferrous objects. For instance, while we have found the field fortifications from the Battle of Aljubarrota, and even skeletons from a mass grave, the only projectiles found during excavations were sling stones. The acidic soil conditions most likely degraded the arrowheads much more quickly than the soil at Towton did. This may not be the case at Agincourt, but it demonstrates that, even when a battlefield is known with certainty, the archaeological evidence is not always a smorgasbord.

This is not to say that archaeology can't be used to prove the location of a battlefield or, alternatively, disprove the traditional location. The relatively recent archaeological surveys that found the battlefield of Baecula at a different place to the traditional location and the survey at Kalkriese (the Teutoburg Forest) that showed the path of the running battle are two good examples of this. The problem is that comparatively little archaeology has been done for pre-modern battlefields in comparison to early modern and modern battlefields, so that there are still a lot of unanswered questions.

I guess the TL:DR to your question is that we don't know yet why there aren't more finds of arrowheads on medieval battlefields. Are the battlefields in the wrong location? Have the arrowheads eroded over time? Was the battlefield picked over thoroughly enough after the battle that centuries of agriculture have destroyed what was left behind? All of these are possibilities.