The knight is a great chess piece because of its famous "L" shaped jump. As you mention, the rose takes this unusual move, and lets it keep going until it forms a "circle". That might be why its called a rose.
Personally I think this piece would be tough to play with. Since a knight can jump to 8 squares, the players need to consider eight different "rose shaped" future possible attack sequences, for each knight on the board.
Anyone can take the infinite chess concept, and modify it for interesting games. It might be fun to try the rose. Unfortunately, right now, I'm a bit busy to try it in a game. But I really like this type of idea, especially for a "test game".
I recently read about the rose, which is a fairy piece that was invented for "Chess on a really big board". Basically it moves like a knight but once it has moved it can move again by basically turning 45 degrees and moving the knight move that is in that direction. It can move any number of knight moves as long as they are legal. Do you think we should add this to chess on an infinite plane?
More info about Chess on a really big board: https://en.wikipedia.org/wiki/Chess_on_a_really_big_board