i think this is an interesting idea, even feasible. My only opposition It is not that easy to find campsite for wild camping in Europe. In most countries camping is not allowed. Therefore you have to sneak in and sneak out from private properties. in some places suck as Germany, Netherlands, Belgium there are so many towns, villages and roads that there are no possible places except city parks. Wild camping is best in Eastern Europe, Poland, Tjeckien, Slovakia. etc
a possible solution for washing and shower could be to go to high end hotels with laundry service. Only if you have a lot of money.