Well, for starters, the Fulmar was never intended to. The RN needed a long range fighter to escort strikes, take down fleet shadowers and provide reconnaissance. And due to the changing understanding of requirements they needed one quickly as a stopgap. Hence the consideration of aircraft that had been designed to an earlier, now cancelled light bomber spec (the Fairey P.4/34 and the Hawker Henley). If the RN had wanted the Fulmar as a strike aircraft they would have had to change the requirements for the TSR specification that was already underway and would produce the Albacore. And while it’s certainly possible that that would have been a better use of resources, it’s not really reasonable to critique the aircraft for not delivering something that was never asked for.The 18" Aerial Torpedo or equivalent bombload. The ultimate purpose of the RN and FAA is to sink the King's enemies ships. This can do that, a Fulmar can't.
Additionally, the OTL battle could not carry a torpedo either. Your Sea Battle had to use a radial to make that work (otherwise the intake is right in the way). But if you are going to be shoving a radial (I am guessing a Hercules based on the timeframe) into something, why the larger and slower Battle rather than the Fulmar?