Idealism is great and all, but you gotta have a practical plan to achieve something.
Multi member districts is not a bad idea for the House of Representatives. Can be done on a local level. But there needs to be a constitutional amendment.
Why not simply switch to a system where a state itself is a giant multi member district, like a parliamentary system?
Because this isn't software... you can't just "switch" to a different form of government like that.
Even, a political grass roots revolution would be unsuccessful as many people are resistant to change and would not back it.
Incrementalism is the best approach as it slowly changes people and doesn't get their defenses up from the get go.
However Congress has barred at-large representation and that law would require changing as well.