I get what you're saying about geography.
But the alternatives have a lot of pitfalls. An at-large candidate from Texas or California is not likely to be particularly close to any minority demographic that might desire a champion for their concerns. You end up with every candidate from Chicago, campaigning in Chicago and its collar counties, and no one ever visits or gets elected from Carbondale or Bloomington-Normal or the Illinois part of the Quad Cities.
It might be appropriate to segment the population by profession, such as to have all the bus drivers, car drivers, train operators, and pilots in the state nominally represented by the same person, while all the farmers, loggers, and ranchers have their own person. That faces the same problems as geographical gerrymandering, and more.
If you segmented the population alphabetically, the representative for surnames starting with the letters A through C does not have a particularly clear mandate. But at least it would likely be a fair distribution.
I think the simplest segmentation would be between urban and rural. Line up voters by the population density of their census tract. Slice the population into a reasonable number of buckets, 2 or 3, and the voters in those buckets elect a number of at-large representatives. You probably end up with liberal representatives for every urban core, moderate representatives for every suburb and commuter artery, and conservative representatives for every hamlet and unincorporated township that can still see the stars at night.
Democracy means representing the majority view tempered by personal judgement.
You could, but that would actually be worse the FPTP in single member districts.
> Logically the choices would resemble the choices of the population.
No, they wouldn't, except by chance. Say you have six candidates, A-F, for three seats. 75% of the electorate prefers an ideology generally espoused by A, B, and C; 25% prefers an ideology generally espoused by D and E, and 10% prefers an ideology espoused by F.
In the first group, A is by far the most effective campaigner and gets 70% of the total vote, with the remainder split evenly between B and C; in the second group, support is split equally between D and E. The last, of course, all goes to F.
So, in your top 3 vote, A and F win seats in the clear, and the third vote goes to a tiebreaker between D and E; this does not at all reflect the distribution of views in the population.
That's why methods like Single Transferrable Vote and it's relatives, using preference rather than bullet ballots, exist.
It's not an interesting solution to the real-time results obsessed crowd, but it is a solution proven to mostly work.
You could simply let anyone vote for anyone and elect the top N contenders where there is N seats.
Logically the choices would resemble the choices of the population.
You can also use the slow but difficult to default distributed network we have had the longest. The US mail.