Back in April 1948 things were different, according to an anecdote I came across this afternoon. The Yishuv was gearing up to declaring independence, and this included delineating spheres of authority for the soon-to-be ministries, and appointing ministers. Yitzhak Greunbaum (1879-1970) was slated to be Minister of the Interior - but he had an objection. The ministry was intended to include overseeing the police, but he had a spot of aversion to police forces: "In [Czarist] Russia I didn't much like the police. In [post WWI] Independent Poland, I didn't much like the police. Here in Palestine, I haven't much liked the British police - and I certainly wouldn't want to be identified with the undercover police!" (Greunbaum was among the leaders of the Yishuv who was arrested by the British in 1946).
So they hived off the police from Interior, and that's how the police ended up with a minister of their own.
Though, as a tragic postscript, there may have been an additional, even darker reason for this aversion. Gruenbaum's son, Eliezer, had been in Poland when WWII broke out, and eventually survived the camps. After the war he was identified as a kapo in Auschwitz, and was arrested and investigated by the French police; the case was eventually closed. A few weeks after his father refused to be in charge of the police, Eliezer was killed fighting in Jerusalem, apparently by friendly fire.