The hill people from Appalachia deserve to be represented by someone local. The low lying coastal communities in the outer banks also deserve to have someone that understands them, rather than someone from NYC. The border towns in Texas are better represented by someone from there, rather than someone from Ohio. There is some value to local representation, it doesn't need to be all in.
Romania for example has a hybrid system: it's "first past the post" first and foremost, so people get local representatives, but all the unused votes that would otherwise get wasted (both winning and losing ones) are then put together in a big national pool and then you have the second round of MPs appointed because of that pool. That way popular vote matches the percentages in the parliament, but you also have local representation.
And think of this. Today House members spend all their time mooching for donations, because to get elected requires a BUNCH of money. That money is increasingly dominated by money outside your district. If we have a Representative for every 20,000 citizens for you 15,000 number, that means you can run a small campaign for very little money. Heck you could just knock on doors for no money.
THAT takes a lot of power away from moneyed interests.
Also, 331,000,000 citizens / 50,000 citizens/rep = 6,600 reps
I agree that uncapping the house would improve things, but I do not think that it is fundamental to improving things.
I don't think we should base our political system on the assumption but I don't think it's unfounded. It's tough to want to have the makeup of my state legislature reflect the will of the population at large while making sure when the pool is distributed my district gets a democrat because anything else would be insane given the political makeup of the area.