On ground attack aircraft, as has been said the P-51 was not really considered a very good strafer. The Brits did use the first lend lease models in such a role but that was before they started swapping out the Allison motors for the Merlin engines and overnight basically changed it to a high altitude escort fighter. With it's liquid cooled engine it was extremely vulnerable to ground fire and was considered much too valuable as an escort fighter to be used in the ground attach role. However combat pilots being combat pilots I'm sure it was done on occasion. My guess as well as others is the movie company used what they could find and there are a hell of a lot more P-51's kicking around than P-47's. But, no, it was never known as a tank buster that is for sure!

On the main topic aircraft were always around in tank battles. You might not destroy many tanks from the air but what you do do is isolate them from their infantry and logistical support elements making it easier for your hunter killer teams to get closer to the tanks to destroy them. In the Germans case far more tanks were lost do to lack of fuel and/or service due to their support elements being destroyed from above then were lost by direct hits from fighter bombers.
Another little tidbit re Patton and Monty. If you notice a lot of Commonwealth tanks have chunks of extra track stuck all over them to combat hollow charge weapons. Patton and Ike refused to allow their tankers to do this because he felt not only was it a waste of precious fuel to carry the extra weight around but that it was not good for morale. Brit officers felt that anything that increased morale was a good thing. If you thought you were safer, you may take more risks in a given situation. The Americans opted for sandbags as supposed protection against HEAT rounds.