The disorder in the Republican conference, with Kevin McCarthy seemingly unable to get a majority of House votes but nobody else clearly able to do it either, will surely renew talk, of varying degrees of seriousness, of choosing someone from outside the House to be Speaker. The Constitution does not, it’s true, explicitly say the Speaker has to be a member of Congress.
Matthew Franck addressed this question in NRO the last time McCarthy was having trouble getting to the Speakership, in 2015, arguing that the Constitution implies that a Speaker has to be a member of the House.
Among his points: Accepting a non-member as Speaker would open the door to letting a Cabinet member be Speaker, contrary to the aim of the Constitution’s incompatibility clause. I’d add that you would also then have the possibility of a Speaker who, unlike executive officers, judges, and the actual members of Congress, had not taken an oath to the Constitution.
Franck ended one of his posts on the subjects this way:
The customary understanding that the speaker must be a member comports with commonsense, natural use of language in context. If you sponsored a boys’ football team and said to them “choose your captain,” it is hardly likely that they would go outside their ranks to make their choice. They would be understanding you to require them to choose, from among themselves, the first among equals to stand forth and speak for the whole team. And they’d be right. It is just possible that one wiseacre would be tempted to try out “parlor-trick textualism,” as I called it, an overworked literalism that defeats the purpose of what was required of those trusted with a decision. “How about my little sister?” But you would be justified in saying, “Pipe down. You know what I meant.”