Alright, Sherman, and where is the provision (Article I, Section 9, Clause 2)? It is an Article I power, not an Article II power. As you should know, Article I sets forth the powers given to CONGRESS. The entire discussion has had to do with Lincoln unconstitutionally usurping Congress’ power in this area. People familiar with this area of the law know that well before 1860 even the federal courts had recognized that this was an explicit grant of power to the Congress. John Marshall, years before, had written in an opinion that “if ...the public safety should require the suspension of [the writ of habeas corpus] it is for the legislature to say so.” By the time of Lincoln there was a line of precedent for this very obvious constitutional point. Lincoln ignored a USSC order telling him to stop his unlawful arrests, and the unlawful suspension of the Great Writ continued for some time (and thousands of illegal arrests) before the Congress voted a suspension.
That the location of the clause in question means that it is inherently and solely a legislative power is certainly a common POV. That it is not the only POV for which a case can be made is shown best by this article.