I like a big one -- a brush ax -- for cutting unsupported branches. Where a machete would nick them and push them aside, the hooked blade grabs and cuts. As a weapon, such a tool would be pretty scary. That forward hook could penetrate or could hook and damage the limbs of an attacker. A small hawkbill is awesome for harvesting from the garden or for cutting other light vegetation. It can also cut tough materials like plastic, leather, etc.
To see a pretty realistic "use" of linoleum knives, see the sauna scene of "Eastern Promises." Pretty much a worst case scenario assault with knives: naked, on slick floors, unarmed against multiple attackers with blades. Scary.
An unusual blade shape will do some things very well and others poorly. Hawkbills make terrible general-use utility knives. Try using one with a cutting board, or try cleaning up saw cuts with a hawkbill (I use a very simple Mora as a woodworking knife). Hawkbills are specialized, not versatile.
I definitely prefer more conventional blade types for carry knives.
Respectfully,
Dirty Bob