that is entirely a self inflicted hurdle, the law used to be there was to be one representative for every 30,000 persons, but then in 1929 congress passed the Permanent Apportionment Act of 1929, fixing the number of representatives at 435. if we had stuck with the original we would have 11,080 representatives. technically speaking the only barrier to this is repealing that act, that and building a much larger capital building
True enough, it's not strictly a Constitutional problem (we don't need an amendment). But going from 435 to >10,000 House members is a massive change.
I've long though that pegging House districts at the population of the smallest state was a reasonable middle ground. That would put us at 571 members instead of 435.