Gutters have to come off for a proper tear-off anyway, and the drip edge and roof edge detail are installed at the same line. Replacing them together means one mobilisation, one crew, and a roof edge that’s detailed correctly rather than worked around.
If the fascia behind the gutter has softened, that’s the moment to deal with it — while it’s exposed and visible.
Chimney flashing and roof penetrations should also be inspected when roof-edge or drainage work is being completed.