Why Nelson accepted the risk of a West Indies pursuit

Was Nelson's decision to pursue Villeneuve to the West Indies unsound compared with joining Cornwallis?

It was risky but strategically defensible, because damaging the combined fleet farther from Britain could reduce the threat before it reached later British defensive layers.

Joining Cornwallis would have been the safer course. A navy cannot always choose the safest option when an enemy fleet remains a strategic threat. Catching and damaging Villeneuve farther from Britain could reduce that threat earlier, even if Nelson's own force paid a price. The reasoning matches the video's layered-defence theme: damage inflicted forward makes the enemy less capable when it reaches the next British fleet.