Yes for day to day living taxes would most likely not be an issue if you had as much money as you mentioned. But what if you have children or others that you want to pass the money along to after you die? If you're not careful they could lose half of it in inheritance taxes. It would be wise to put that money into a trust and for that you need professional help, unless you happen to be an accountant or attorney.
Personally, I might think about setting up my principle residence in a place like The Bahamas where they have no taxes. You could still rent places in Paris or NYC or Milan or wherever you like but just keep a home base in a low tax or no tax location. One thing about multiple residences though - you need someone to look after it when you are not there. And if it's a house then you need someone to do the landscaping and take care of the pool, etc. You'll probably need a vehicle in each place as well. I'd probably opt for a nice lock it and leave it condo with security staff. Come and go as you please.
A pretty awesome lifestyle to be sure but not without its own set of problems.