Sure. They just happened to stick it in a list of things Congress can and can't do, in the article that defines and establishes Congress, and before the article establishing and defining the executive. What sense would it make to give the President the ability to unilaterally suspend oversight of himself? Can you really see the founders of this country doing that?
And right next to that section in the same article that says what states may and may not do, so it's clear that Article I did not apply solely to Congress. In other sections of the same article, the Constitution clearly states that Congress shall or shall not. So such words were used in section 9. Until the matter is brought before the Supreme Court then the question of who exactly may suspend habeas corpus remains undecided.
What sense would it make to give the President the ability to unilaterally suspend oversight of himself? Can you really see the founders of this country doing that?
Yes. You have to remember that up until the middle of the 20th century Congress was a part time occupation, usually meeting for only a few months out of the year. In the event of a rebellion or invasion when Congress was not in session then the president should have the power to act to protect the country. That is why, I believe, the specifics of who may suspend the writ were not specified. And also why the Constitution specifically limits the reasons why it may be suspended.