The president's powers go far beyond the list you wrote, Cogman. You forgot a few of the most important things.
First and foremost, the president is also the true leader of his party. And the party usually follows their leader (especially with the unwritten pact that the republicans have had for quite a while). For six years, the president controlled the house by being the leader of the party in the majority. For six years, the president controlled the senate by being the leader of the party in majority. For nearly eight years, the president controlled the executive branch, by well, being the president. What that means is what the president wanted, he almost universally got.
Take NCLB for example. Bush campaigned hard in the 2000 elections based a lot upon NCLB. As soon as he took office, he got his fellow republicans to pass the NCLB bill that he wanted. Then he signed it into law. Yes, you could ignore his influence on congress, but you'd reach very incorrect conclusions.
The patriot act was similar. Bush wanted it, he got it. Many of the members of congress had only hours to read a massive bill spreading across many pages. Congress had no idea what they were voting on for the most part. Then Bush signed in into law.
Also, yes, the constitution gives budget authority to congress. But congress turned around and gave that authority to the President starting with the Budget and Accounting Act of 1921. Yes, the act has been altered many times, but the result is the same. Congress, BY LAW, gave the original budget proposal authority to the president. By law, Bush writes the budget. Then congress can make minor modifications before Bush signs it. But with Bush being the leader of congress, congress didn't make many modifications. So Bush pretty much had control of every step along the budget process. Just as a CEO of a company gets blamed for company financial problems, so does the president. Heck, he took credit for the housing boom, he should get blamed for the housing bust.
It would be slightly different if Democrats had the majority in the house and senate during most of his time. But still, Bush signed into law each and every one of those problem issues that you mentioned. He could have vetoed them. If congress overrode his veto, THEN you'd have a case about not blaming the president. However, that situation just didn't happen. Bush basically had a major say in writing and signing every law that passed.