No, you said a moderate Republican could never win the White House and I said that plenty of moderate Republicans have won the White House. As far as I can tell, the only conservative Republican who has ever won the White House was Reagan.
Of course, plenty of moderate Republicans have lost the White House. No argument there. I don't know how many conservative Republicans have lost because it seems we rarely ever nominate one. Maybe Goldwater (but by today's standards he'd be a solid Libertarian).
No moderate will ever win.PERIOD!
Calvin Coolidge and William McKinley were conservatives.