The problem with filtering the whole system is that the rate of flow would be very slow through shower or wash basin taps, it is not fast through the drinking only tap that we have but is fast enough, but the thought of running around in the shower trying to find the relevant drip would be very daunting!
Is there a particular reason to filter the whole van? If it is because you are likely to fill up the tank with polluted water it would be better to either find a better source or to treat the water before putting it into the tank IMHO.
As has been said above, the life of the filter would also be shortened considerably, and they are not cheap. With average use they last about 1 year, but with full van use that would be considerably shortened and in hard water areas would be very short as the filters do tend to clog up with scale from our experience.
Since the way of knowing it is time to change the filter is when it gets too slow you could find the whole van concept to be very counter-productive.
Good luck and do let us know - particularly if there is another reason why you want to do the whole van.