Animateness-neutral "its"

The House of Representatives shall chuse their [modernly, its] Speaker.

U.S. Const. art. I, § 2

Wouldn't the use of its here be "animateness-neutral", so to speak, as opposed to their?

Solution 1:

This is not a singular they, as your tags imply it might be, but a plural they. In modern American English, we usually treat collective nouns as singular. "The company puts out a press release most weeks, but it skipped this week."

In the usage you quote (and sometimes in modern Commonwealth English), the collective noun is being treated as a group of people. "The company put out a press release most weeks, but they skipped this week."

Solution 2:

The quoted sentence is using "House of Representatives" to mean members of that body. So the plural pronoun is perfectly appropriate, 232 years ago and now.