The issue of logistics is a large one. Training an archer takes quite a long time in comparison to an arquebus, and training a GOOD archer force takes practically a lifetime (see: Medieval England). It is, in short, extremely expensive and difficult to maintain a large pool of archers, and archers, in comparison to arquebusers, are much harder to replace as they are attrited away in any real campaign (especially the variety that could make a significant difference in battle, i.e. longbows. The English had to implement extraordinary subsidies and benefits to encourage bowmanship). More to the point, while highly skilled longbowmen, for example, could potentially put out a higher rate of fire, both RoF and overall archer performance depend greatly on the archer's health (which, in campaigns, is most certainly subject to deterioration), and, their RoF will certainly decrease throughout a battle due to fatigue. Moreover, building an arquebus and providing ammunition for it is far cheaper (and easier [bullets vs arrows]); yet another great blow to the bow.
Another issue was armor. As the Middle Age progressed, both the increased prevalence and quality of armor on even common infantrymen significantly reduced the lethality of longbows, and bows in general. Thus, arquebuses were becoming increasingly lethal, whereas bows lost ground to both guns and crossbows (the latter being phased out due to cost).
Arquebuses were also far most useful in close-combat situations. That is, a bow is virtually useless if an enemy gets close, and an arquebus could be used to club someone to death. It was also far more useful in fortified positions, as the arquebus allowed the soldier to take cover, and is in general far less unwieldy then the bow in confined spaces.
In short, the bow's obsolescence couldn't really be delayed. Guns were, in effect, cheaper to produce, far better in close quarters and fortified positions, far easier to use, far easier to supply,
and more lethal.
'sides, shot n' pike (or was it the other way around?) sounds better than arrow n' pike .