I entered the following puzzle in SudoCue, and clicked on Optimize - Keep Symmetry. It didn't find a more minimal puzzle. However, if you remove the 5 from the center square, the puzzle is still valid and symmetrical.
I think I might understand what's happening. In this case, when the Optimizer removes the center clue, the Analyzer score indicates that the resulting puzzle is easier than the original. I don't think that it should work that way. When you remove a clue from a puzzle, the puzzle always gets harder. The Optimizer should not compare the Analyzer scores of two puzzles where one puzzle is the same as the other, except for having fewer clues.
It turns out this isn't a bug. Removing the center clue results in a puzzle with multiple solutions. I didn't realize it because the Analyzer results looked the same as for valid puzzles, due to an apparent bug in the Analyzer which causes it to terminate prematurely on some valid puzzles. I think that this is the same bug that I reported in the "Problems with Analyzer" thread on this forum.