Climbing without leg spikes demands considerable strength and skill. A spike climber can create a foot hold where ever he stabs a leg spike. A spikeless climber throws a rope over a branch and literally pulls himself up using the rope. Just the art of looping a rope over a high branch excludes most tree climbers from climbing spikeless. You might have a hard time finding a climber who doesn't use spikes.
Some situations do warrant the use of leg spikes.
Dead trees do not pose a problem for spike climbing. The tree is dead so no further injury can occur, and spikes provide the climber with more security by furnishing foot holds as opposed to fragile dead branches. A climber may use spikes while climbing storm damaged trees as well. A climber must be able to avoid broken branches, and spikes increase the alternatives in route finding. Climbing small trees with branches too small to support a climber might force the use of leg spikes.