I hate to tell you you're wrong, but...You're wrong.

From this article: https://www.businessinsider.com/who-leads-the-house-mccarthy-ousted-speaker-pro-tempore-2023-10?op=1

"The Speaker pro tem could stay in the chair," Josh Huder, a senior fellow at the Government Affairs Institute at Georgetown University, wrote on X, formerly known as Twitter. "There's not [a] forcing mechanism for a new election, nor are there any overt restrictions on the power the pro tem would wield. The support of the conference would dictate the durability of this."

From this article: https://www.usatoday.com/story/news/politics/2023/10/04/mccarthy-ousted-who-is-speaker-of-the-house-who-is-running/71055124007/

Can the House function without a speaker? Formally, yes. But politically it can be complicated, experts said.

From everything I'm reading, technically, YES, the House can function as normal - the reason it may not is because politically, McHenry was not voted into his position so he has to act like he does not have the full power the SOTH would. Ask Nancy Pelosi and Steny Hoyer what THEY thinks about it - they sure acted like McHenry had the authority to make them move offices. The whole reason for having a pro-tem position is so that business can move forward in case of a vacancy.

A guide to the House rules states:

...the House speaker pro tempore “may exercise such authorities of the office of speaker as may be necessary and appropriate pending the election of a speaker or speaker pro tempore.”