"I don't understand the obsession with rewarding states for having small populations and punishing those with large populations."
Categorizing it as an "obsession with rewarding [...] and punishing" is frankly reflective of the fact that you never tried to understand it. No one is doing this.
"The state with the most farms and resource extraction is Texas. Texas is a large state. The most urbanized states are DC (not a state but acts like one in EC), and Rhode Island. Both are focused on a single large city: Washington and Providence Metropolitan Area. Both are small states."
You are cherry picking examples that break the mold. Here's an article on Slate from 2012 discussing agriculture in the US and world. The first map shows the density of farmers per 1000 people. You will see clearly that America's farmland is concentrated in Montana, the Dakotas, Nebraska, Kansas, Oklahoma, Texas, Colorado, and to a lesser extent Missouri, Iowa and Idaho as well.
http://www.slate.com/articles/technology/future_tense/2012/06/a_map_of_farmers_in_the_u_s_and_world_.html
Those states combine to claim 94 EVs. Texas has 29 of them by itself. The remaining 10 states in that list average 6.5 EVs apiece.
Meanwhile, here is a list of the top metropolitan areas in the country:
https://en.wikipedia.org/wiki/List_of_metropolitan_areas_of_the_United_States
You'll see that the first 25 metropolitan areas have a population exceeding 160 million people, which gets at the point of the map in the OP (which shows the smallest geographical area that holds half the country). They are from the following states/districts:
New York
New Jersey
Pennsylvania
Connecticut
California
Illinois
Indiana
Wisconsin
District of Columbia
Maryland
Virginia
West Virginia
Massachusetts
Rhode Island
New Hampshire
Texas
Oklahoma
Delaware
Florida
Georgia
Michigan
Washington
Arizona
Minnesota
Ohio
Colorado
Oregon
Missouri
North Carolina
South Carolina
These states have a combined 426 electoral votes, for an average of 14.2 EVs per state.
Even with the electoral college's built-in skew toward small populations and away from large populations, the bulk of the college's EVs are still concentrated in the cities. I'm not even sure what point you were trying to make by cherrypicking those examples, but you make my point even more about the danger of rural areas being underrepresented by raising DC as an example. DC is **one city** that is literally treated like a separate state (such as, say, North Dakota) for the purpose of winning the presidency.
That is, broadly, how it should be. Most people live in cities, so the electoral college should still have its EVs skewed toward states with the most/biggest cities. The college just makes sure that it's highly improbable that you can win an election with JUST cities -- meaning your presidential campaign has to deliver something for the rural communities which keep our country running.