How absurd.
The axe is still the preferred tool for the backyard wood pile. Not everyone splits enough wood to make a hydraulic splitter pencil out.
But aside from that it's still an important tool among natural resource workers. For a small blow down or storm fall I can have it cleared with an axe before my partner can get his chainsaw chaps on and dig the saw out of the tool box. Then there are the wilderness areas where they won't allow combustion engines, not that you'd want to pack one up there (along with it's associated fuel and bar oil). And most public land managing agencies won't allow volunteers to run a chain saw for insurance reasons. So the axe and the crosscut have to take up the slack.
No real use? Maybe not for you but there's plenty of work still out there for the axe.