I would generally agree with this statement.
The problem is, how does one accomplish a truly objective, non-biased method of doing this? Any solution will be thought up by people. People with opinions. People with biases. People with political and financial conflicts of interest. People who will manipulate the data surreptitiously while pretending to be objective.
If I had a viable solution for that, I'd be doing more than sitting here discussing politics with strangers on the internet.
Some people try to suggest using non-partisan districting boards, but those then cause Democrats and Republicans to try to gain control of them more indirectly, and then it's harder to fix than simply electing new people. That said, they still do at least limit the mischief of gerrymandering.
Probably the best way to do it would not be to change who makes the maps, but change the
requirements for the maps. Right now, congressional districts have to be of nearly equal population within a state; you can't have one district have 500,000 people and another have 10,000, you need them to have nearly the exact same population. While gerrymandering is obviously still possible even with this requirement, it's nevertheless harder to pull off.
So someone could make some kind of geometrical requirement. For gerrymandering to work, you have to have a lot of "line turns" rather than straight lines, so you could simply require that maps have the fewest "line turns" known to be possible (so for example, if it can be demonstrated how to make a bunch of square-shaped districts, you can't use hexagon-shaped districts due to there being more line turns). Anyone can submit a map and whichever one has the fewest line turns becomes the map (if there are ties, the legislature can choose one, but obviously the ability to gerrymander is substantially reduced as a result of this).
Another geometrical requirement I saw someone suggest (
here) to end gerrymandering would be "the average straight-line distance between each person’s residence and the geographic center of that person’s district shall be the minimum known to be possible at the time" which would also seem to solve the issue.
Regardless of what one chooses, if there is an objective geometrical requirement like this (in addition to the already existing requirement of the districts being of nearly equal population within a state), then the ability to engage in gerrymandering is dramatically curtailed. The less ability legislatures have to control the district borders, the harder gerrymandering is.
Two other options are to make representative elections into at-large elections; people vote for a particular "slate" of representatives, and the slate with the most votes wins. This is effectively what almost every state does in the Presidential election (yes, you select a Presidential candidate on your ballot, but what you're actually voting for is a slate of electors who go off to vote for the candidate you chose). This is actually how it was done n some states long ago, I think. The other more modern idea, which various countries do, is to do it via proportional representation, where each person votes for a party and the seats of a state are distributed among the parties accordingly (if one party gets 40% of the vote, they get 40% of their state's seats). Since both of these abolish congressional districts, gerrymandering is obviously impossible. The downside of these options, aside from being a bigger change to the system than simply adding geometric requirements, is that it means the representatives are no longer tied to their districts and no longer have a specific group of constituents, but gerrymandering minimizes their connection to their district anyway (one could do a mixture of districts and proportional representation, which is generally what countries with proportional representation do).
My pastor tells a story of a baseball coach he had when he was younger that would tell his players to lean into the ball. The players would protest, "But that's against the rules". His response? "Lean into the ball, but don't make it obvious". That's my fear with any ostensibly "objective" methodology that purports to eliminate gerrymandering. I have this sneaking suspicion that someone's learning into the ball without making it look obvious.
How does one lean into the ball to solve the geometrical requirements to stop gerrymandering? Even if they could still manage some limited gerrymandering in spite of that, it would at least dramatically curtail things.