Smaller districts, because of geographical sorting, or spatial covariance, or however you'd like to describe it, would be more homogeneous, and that is EXACTLY the point. What matters is that Representatives better reflect the opinions and beliefs of their constituents, not just the half that won the election, and that the people know their representative, and that the Representative does not need to depend on large donations in order to speak to those people.
What you implicitly describe as a strength, competitive districts, leads to winner take-all political dynamics and MORE extreme politicking, and leads to districts that are perpetually unhappy with their representation.
And in aggregate, the less the party and President can influence a Representative's re-election chances, the more independent that Representative can act, and the more that Representative can reflect their district's particular beliefs. This is a moderating dynamic. In fact, it threatens the two party system in the House allowing cross-party. They can try to be as disciplined as they want, but if they have little leverage over its members, then it will be a fruitless endeavor.
Re: govern-ability of a large House. This is repeated over and over, yet it seems more about opinions and reinforcing the status quo, which is not working, than evidence. And the larger point is that we need to start with the purpose of the House. First fulfill that: To Represent their Constituents faithfully. Without that, none of the other stuff matters. Working efficiently for the wrong ends is not winning.
In terms of the UK, while the ratio in the UK is 100,000 citizens per MP, for a citizen to be a candidate for MP, their Party must approve them, or at least, not veto them. That is not generally true in the U.S., and only true to the extent that the party can send ad money to someone else in the primaries. I think there is good reason to think that smaller districts in the U.S. would give weaker control to Parties, not stronger control.
You are correct that major local employers and NIMBY groups can dominate in small districts. Do they not now? Between begging for money from every monied power and hoping to avoid the ire of the Party and President, where does that leave the Representative in terms of representing their constituents?
In the end, I just don't find myself convinced by these objections, but I do thank you for your considered response.
