For most alpine skiers, straps are essential and going strapless isn't recommended. Straps help you plant your poles with confidence, keep them from dropping in the snow if you lose your grip, and actually reduce fatigue by letting your hand rest between plants. Without straps, you're constantly gripping tight, which tires your hands out fast.
Strapless poles do have a niche, though. They're popular in Nordic walking and some freestyle applications where you want maximum hand freedom and no risk of strap-related thumb or wrist injuries in a fall. If you're a park skier who frequently drops poles before hitting features, strapless grips can make that quicker.
The big trade-off is convenience versus security. Strapless poles are easy to ditch in a crash, but they're also easy to lose mid-run when you brush a tree or take a tumble. For resort skiing, the safety and control that straps provide far outweigh the freedom of going without. If strap injuries are a concern, look into Leki's Trigger release systems instead—they give you strap security with injury-preventing quick release.