One of the main reasons an amphibious invasion of Britain was near impossible was because the German navy could not contend with the British navy and provide a large enough landing ground and secure supply chain. Was there any reason why German high command didn't employ German U boats to sink British destroyers and other battleships to weaken the royal navy?
The U-Boats were brutally outmatched by the British Royal Navy. Germany started the war with 56 U-Boats, not all of which were combat capable. The Royal Navy had, in 1939, 15 battleships, 7 Aircraft Carriers, 66 Cruisers, 184 Destroyers, 60 Submarines, and 45 misc escort vessels.
Additionally, u-boats are fairly ineffective against destroyers and other small naval units due to the speed, maneuverability and small target area. Although u-boats did sink destroyers, it's a fairly even match and destroyers also took a heavy toll on u-boats. Allocating the u-boats to the commerce destroying role was actually probably the most effective strategy, since it forced destroyers to be tasked with convoy escort and took some of them out of home waters.