Yes, that's a hopeless circuit for driving motors, it's quite good at burning out
Switching devices for power should be driven to saturation, the top transistors
in that circuit are emitter followers and without a bootstrap-supply for the base drive
so they will get hot and waste a few volts.
More importantly without flyback diodes it will simply destroy itself through
inductive kick-back spikes.
Single IC solutions are much easier to use, but if you want a better BJT circuit
with saturating transistors and flyback diodes, how about:
The layout's a bit odd, the H has been twisted over between top and bottom drivers
to show how the input transistors switch on one NPN and one PNP. Only two input
signals are needed, but they must not be HIGH at the same time of the bridge is
shorted out ("shoot through") which will destroy it. A full-wave
rectifier chip cleverly provides all 4 flyback diodes in one package.
Super-beta transistors have been chosen (its an all-surface mount design though).
resistors R5 and R6 are chosen to match the drive level and supply voltage, the above
values correspond to 6V supply with 20mA of base drive to the output transistors
(which have gain > 250 I think and several amps max). With more humble
transistors the max load will be less and R5 and R6 should be chosen for more like