Ski poles with a small, integrated ice axe are quite common in North America but quite rare in the Alps. These are not only intended to help you conquer steep passages, but also to act as a brake in the event of a fall. The most widely used model is manufactured by Black Diamond and goes by the name of Whippet.
The pickaxe pick of the Whippet is permanently attached to a two-part telescopic pole with the tried-and-tested Flick-Lock system. If you don't need the ice axe, it can be "disarmed" with a plastic cap.
In practice, you will of course use the Whippet as a simple ski pole most of the time. Apart from an imperceptible increase in weight, there is hardly any difference to a conventional ski pole. Of course, you should avoid falling on the pole as much as possible. Even if the tip is covered by the plastic cap, you still have a hard, sharp tool in your hand.
The integrated ice axe is particularly useful for ascents in steep firn or harder snow. The tip grips easily and provides a good grip. Especially in combination with a proper ice axe, it can also be used to conquer really steep sections. In real ice, however, the blade of the Whippet has little grip, as expected. The ice axe in the pole is also useful when crossing steep firn slopes during the ascent on skis. Of course, crampons are more important here, but the ice axe in your hand still provides additional safety, while you would hardly take the real ice axe out of your backpack.
What I wouldn't trust would be to hold a fall during a descent on skis in steep terrain with the help of the Whippet. This is already difficult to do with a real ice axe, but I haven't tried it...
In the end, I don't take the Whippet with me on tour too often, but it has become standard equipment on long spring tours, steep ascents and longer undertakings such as ski crossings or expeditions.
Conclusion
Special, but if you assess the possibilities correctly, it makes perfect sense. Does not replace an ice axe, but is still always useful.