Why did falcata style weapons disappear?

[Tyrfingr]

As already mentioned, the "falcata style" sword was used through the Dark Age, into the Middle Age and on to near-modern times. (Falcata > Falchion > Sabers)

[Philippus Flavius Homovallumus]

The Bill, more properly "billhook" is a concave cleaver which we use for stripping trees/hedging etc. They come in a variety of styles, some have the back spike but generally the farming implement is purely a hook-and-blade affair, with a short handle.

A quick search turns us this: http://pilgrim.ceredigion.gov.uk/ind...articleid=1564. As you can see they come in a variety of styles, unique to regions of England and Wales, and have short handles.