For one, he or she can nominate Supreme Court judges. This alone is huge, considering the SC is the final arbiter in the most important conflicts in the nation.
Aside from that, he or she can issue Executive Orders, which "have significant influence over the internal affairs of government, deciding how and to what degree legislation will be enforced, dealing with emergencies, waging wars, and in general fine-tuning policy choices in the implementation of broad statutes."[1]
The POTUS can also veto legislation passed by Congress. Historically, Congress has been able to override these vetoes only 7% of the time[2], which means the POTUS has a serious amount of influence in the direction the country goes in as well.
And of course, he or she is also the Commander in Chief of the world's most powerful military, and the country's supreme representative in foreign affairs.
Bottom line: POTUS is much more than a "punching bag."
[1]https://en.wikipedia.org/wiki/Executive_order_(United_States...