The main reasons are two:
- lack of mobility
- effectiveness of the engagements
If you go for such an army comp you have to chase them and your opponent can pick whatever fight he pleases.
The second reason is that, while plumed archers kill longsword, the same can’t be said for skirms with eagles. Your longsword would get picked off by the plumes, while yojr skirms would just tickle the eagles. Even if you manage to engage, eagles + plumed literally kill longswords + skirms with no micro neeeded.
Also, what I wrote remains 100% true even if you switch the plumes out and sub in xbows in their place