History Lesson.
Why do we have a limit of 435 members in the House of Representatives?
The U.S. Constitution Article I, Section 2, guarantees each state, territory or district at least one representative and further states that there can be no more than one representative in the House for every 30,000 citizens.
So there is NO Constitutional cap, but the size grew quickly over the next century based upon rapid population growth, mostly from immigration. When the number got to 391 around 1911, Congress passed the the Permanent Apportionment Act of 1929, which set that number at 435.
The reason for the cap is interesting then and now and hidden in the middle of the quoted reference. I will give you a hint — it had something to do with competing interets involving urban, rural, and foreign populations. From ThoughtCo.com is the following,
“The Permanent Apportionment Act of 1929 was the result of a battle between rural and urban areas of the United States following the 1920 Census. The formula for distributing seats in the House based on population favored “urbanized states” and penalized smaller rural states at the time, and Congress could not agree on a reapportionment plan.
“After the 1910 census, when the House grew from 391 members to 433 (two more were added later when Arizona and New Mexico became states), the growth stopped. That’s because the 1920 census indicated that the majority of Americans were concentrating in cities, and nativists, worried about of the power of ‘foreigners,’ blocked efforts to give them more representatives,” wrote Dalton Conley, a professor of sociology, medicine and public policy at New York University, and Jacqueline Stevens, a professor of political science at Northwestern University.
So, instead, Congress passed the Permanent Apportionment Act of 1929 and sealed the number of House members at the level established after the 1910 census, 435.”
See How Many Members are in the House of Representatives?