I think you’re understating the power of the Presidency here. For one thing, they have veto power over Congress.
For another, many laws are broad and give a lot of leeway for interpretation, which is why presidents can accomplish a lot by executive order. As long as the Supreme Court doesn’t step in anyway.
And third, don’t underestimate the power of the bully pulpit. Presidents are looked at as the leaders of their party, and often set the legislative agenda. If a president says they want something done, their party members in Congress will find a way to get it done.