Why the Royal Navy did not need a Constitution-style heavy frigate

Would the Royal Navy benefit from adopting a Constitution-style heavy frigate first?

Not greatly, because Britain already had larger ships that filled the firepower gap and could defeat heavy frigates directly.

A heavy frigate offered a smaller navy a powerful cruiser killer when full ships of the line were scarce or unaffordable. Britain already possessed fourth rates, razees, and third rates that could overmatch such a ship. Its strength against ordinary frigates therefore became a liability once a larger fleet deliberately assigned a line-of-battle ship to hunt it.