Never had room for a fresh water tank, so used a hose pipe, have been doing this for 6 years now, and yes when there is no outside tap I use the kitchen/sink/bathroom tap, which ever is best fit.
You learn to adapt your system to suit.
However never in 6 years have I arrived and started within 4 minutes. Pre inspection springs to mind, then vac, then prespray, then setting up etc