Consider what the purpose of this counter is in the larger circuit. If the purpose is to generate the four "counting"-waveforms, and if you can guarantee that the clock signal is well controlled with a 50% duty-cycle, then yes, you could concivably use a 3-bit counter.
However, the output of a counter like this is usually used as an input to some other circuit (such as a decoder, or as an adress to some sort of memory). In these cases, you want a full clock-cycle to elapse for each combination of the output lines, so that the larger circuit can do something with each of the combinations. This requires the clock-signal as an extra signal, and requires the least-significant bit of the counter value to oscillate at one-half the frequency as the clock.