Two approaches to consider. Empirically you found the first one, essentially using a very slow square wave. Your system will most likely have some characteristic time scale to reach steady state, if you make your on/off cycles much longer than this, you can get the information you want. Technically you can't point to it and say "this is the step response", but you can get the same information (ie. the transfer function). The approach I suggest, however, is to recall that in the time domain, the derivative of the step response is the impulse response which is much easier to deal with in the finite FT.
If you are trying to, for instance, get the transfer function of a system by dividing the FFT of the output by the FFT of the input, then your input better have components at all frequencies you are interested in. If your input is a sine wave, you'll get your transfer function at one point. As you have seen, if your input is 1,1,1,1,1,1 you get the dc response. The impulse has equal components at all frequencies included in the FFT, so it is very efficient to use it to determine the transfer function.
I am not a DSP guru, nor do I play one on TV, but that is my 2 cents.
