Why third rates did not dominate the frigate war of 1812

Did the Royal Navy consider sending third-rate ships of the line against American frigates?

Yes, and some arrived, but transatlantic redeployment took time and American frigates generally avoided a 74-gun opponent.

The Royal Navy did send some third rates to American waters. Sailing orders, preparation, and the Atlantic crossing delayed their arrival until much of the celebrated frigate fighting had already occurred. Once present, a 74-gun ship presented an opponent the American heavy frigates were designed to outrun rather than fight. The strategic effect was therefore often denial and confinement rather than another balanced single-ship duel.