How? When people complain about money in politics issues these days, they're usually complaining about 3rd party money. I don't see how having 100x more representatives would reduce 3rd party money. It's not like it's hard to target 3rd party ads to small geographic areas.
What makes you say that? Hell at 10,000 constituents you borderline don't even need to run ads, just go door to door, personally.
EDIT: Although I suppose the tactic could at that point be turned to buying voters more directly. Spend a ton of money on something that benefits everyone in the district and make it clear that it'll keep coming only if they vote for your candidate, and you might have the same effect.
You could probably get the same result by blocking funding external to the district and killing citizens united. And/or shorten campaigns to 60 days so they just don't cost as much. And/or, provide public funding and election spending caps.
I don't think that trying to scale out of it would be that effective but I see what they are getting at. My guess, is that would raise the inequality of the playing field again as the richest would be able to spin up an organization to manage 10k reps, decide whose relevant who to fund, and so on, people who didn't have lobbyists before won't be able to afford that even if the per rep cost gets cheaper, the total influence cost will rise and price additional people out of the market.
Candidates are far more concerned about 3rd party money than direct donations these days, because 3rd party spending is unlimited. Quid pro quo is not necessary because it's all done in public. You don't need a secret meeting with a lobbyist to know if the NRA likes your position on guns. Just watch the ads.
Of course not every House member has to worry about this; in fact most don't. Most of the big spending on House races is concentrated in the few districts that everyone expects to shift the balance. This would still be true in a House of 35,000. While most races would probably get less expensive, there would still be a small set of "tipping point" races that would attract most of the effort and money.
Quite a lot of House races are on "auto pilot", politically--that is, there's not much suspense about which party's candidate is likely to win. This is in part because of gerrymandering that produces districts favorable to one party vs another.
Tiny districts would be like gerrymandering on steroids. It wouldn't take much fancy geometry to produce a map in which the vast majority of House races remain easily predictable. And it is the marginal (unpredictable) races that atract the bulk of the big spending.