The original "compromise" is that each State gets at least 1 seat in the House, and equal representation in the Senate (2 seats). That is separate to the 3/5ths "compromise" related to the voting franchise.
The house of representatives was always supposed to grow with the population. This changed in 1929 due to an Act of Congress to limit the total to 435. Unsurprisingly, it was done because a Republican Congress would lose representatives otherwise. [1]
What has happened is that by artificially limiting the size of the House to 435 representatives, areas of greater population density are now under-represented.
In a rough approximation:
1. The House is supposed to represent the people
2. The Senate is supposed to represent the States
3. The POTUS is supposed to represent the nation to other nations.
Due to the now unrepresentative nature of the House, the people are under-represented in that balance.
The fix would be to expand the House membership, effectively by using the minimum size of a seat (eg the smallest State is guaranteed at least 1 seat in the House and seats cannot cross state lines).
That size could be used to determine the number of seats in total.
Based on that, the number of seats would be somewhere around (US population / Wyoming) = (328m/578k) = 567 seats.
Personally I would be happy with making house seats exactly proportionate to actual population and adding one senator for every 5 million residents.
So North Dakota with fewer than 800k people gets 2, Washington State with 7.6M gets 3, California with 39M gets 9. This still gives ND 1 senator per 400k while CA has to settle for one per 4M but this is better than one per 20M.
So what? This is the result of a compromise established in 1776 to keep states with lower populations from unilaterally deciding to leave the Union when they lack representation. Do you propose ammending the constitution?