I'm not sure that you can be 'de-princed' (or de-princessed) under the British system, Rudolph. I know that King George V did so in 1917 to some of his relatives when he removed their princely German titles and gave them (lesser) British ones. However, in modern times, with the exception of Princess/Lady Patsy Ramsay (who removed her royal title by her own wish) I know of no male or female born a prince or princess of the House of Windsor (or Hanover or Stuart etc for that matter) who have had that particular style of address removed from them.
You most certainly can. Not only 'de-princed' as we have seen with the Wessex children. You can also be 'princed' as we have seen with Charlotte. Just a few short years ago she would have been Lady Charlotte. She is as we know HRH Princess Charlotte of Cambridge.
In 1917, George V issued letters patent that precisely regulated these matters, specifying that a certain set of individuals were exclusively entitled to certain styles. Before 1917, styles and titles were regulated by a mixture of partial rules and customs.
But Letters Patent don't bind future monarchs, The Letters Patent of Queen Victoria didn't bind George V. Most importantly Letters Patent aren't the only way to create a Prince or Royal Highness unlike a Peer.
Common law has evolved in such a way that the Queen is free to style her family in the manner she chooses. IT's part of royal prerogative that's outside court challenge.
Prince:
This style "is purely a courtesy and the holders of that title remain commoners until they are raised to the Peerage, the only exception being the eldest son of the Sovereign who at birth or, as in the case of Prince Charles, at his mother's accession to the Throne, immediately becomes Duke of Cornwall" (
H. Austin Strutt, assistant under-secretary of state, in a memo dated June 17th, 1954 prepared for the Home Secretary; HO 286/50).
Contrast this with a peer. Holders of peerages are not just recipients of honours emanating from the sovereign, they are called to play an important constitutional role. For this reason, the dignity to which this role is linked has become part of constitutional law, and around it has grown a substantial body of law defining and protecting the rights and duties of holders of peerages. In particular, a peerage may only be created in a very specific form (by letters patent passed under the Great Seal) on government advice; holders of peerages cannot be deprived except by an Act of Parliament; peerages may be resigned only under certain procedures defined by statutes; etc.
Back to Prince George. Under Common Law being a prince doesn't give a person any rights that the average joe doesn't have. Prince Harry has no more legal rights than Peter Philips. William by virtue of being a Peer does.
The title of prince has been used in Britain solely to denote descent from a sovereign. Who, exactly, was so designated, has of course varied with time,
George doesn't use one of his father's title as a courtesy simply because he has his own title of courtesy 'Prince'