Lazy full-bridge PWM control
Edited after clarifications.
This mode of operation is not so unusual for DC motors. Effectively, it is a buck converter, with the fixed side of the load attached to V-. Thus it shares some pecularities with the buck converter, such as discontinuous current mode operation (DCM).
The difference is if you want to reverse direction.
In your operation mode, you either accelerate when the high side is on, or you do low side braking.
If you alternate both half bridges, you either accelerate forward, or accelerate backwards.
When current is low, your operation will result in DCM and a reduced braking torque. For the regular H-bridge operation, the torque will be constant as current goes through zero, avoiding DCM.
However:
Dead-time is an issue even in your operation mode ! Actually acting with both H-bridges, does not complicate the dead-timing. Dead-Time needs to be obeyed on a single leg basis.