I like the idea of a 'rearrange' key too, somehow it does something that 'shuffle' doesn't
Personally, I have to write the letters down into a square (as you see in similar newspaper puzzles). After finding as many words as I can, I write the letters down as shown in my square from side to side, then again up & down. It often helps me find a few more words.
If I do bother entering my words into the online puzzle, I sometimes use the shuffle function with a few letters at a time. I would definitely use a rearrange function.