Perhaps. However, eliminating US House of Representatives districts will require a constitutional amendment.

The way the membership of the House is defined in Article 1, requiring that there be a rep for every x population (where X is set by statute by Congress). It has been long held that this means that each Rep represents those x people, not the entire state, which pretty much mandates election by district.

Also

A number of states set up their state legislatures as mirrors of the US Congress, with a bicameral legislature and one side elected by equal population districts and the other side elected at large.

However, between 14A, the various other voting rights amendments and the Voting Rights Act, the US Supreme Court ruled that states were not allowed to have state legislators elected at large or by geographic districts not based on equal population.

1) There is a parallel partisan gerrymandering case from Maryland, a Democrat controlled state.

2) I fail to see how SCOTUS getting involved in an issue that has no objective non-partisan solution is preferable to what you are warning against here.

“Senate Republicans should invite House Democrats to negotiate an anti-gerrymandering civil rights bill both sides can live with.”

Turning partisan gerrymandering into a civil rights issue will end up being a solution no one can live with.

“States could be allowed leeway to experiment with methods to curb gerrymandering, eg non-partisan commissions..”

They already have leeway to do this. several states already use such commissions.

“guidelines against ignoring county, town, and ward boundaries, etc.”

Requirements that all districts be as close to equal population as practicable likely makes such a guideline unworkable.

(1) It invites Democrats to write a sharp-elbowed, hyper-partisan version of a “voting-rights act” in 2021, should they win both Congress and the White House in 2020. The previous bipartisan “voting rights act”, written to protect Black voting rights in recovering Jim Crow states, established a 14th Amendment precedent allowing Federal intervention in State elections.

(2) It is likely to increase the partisanship of State Supreme Court elections in States (eg Wisconsin) where a popularly elected governor is blocked by a legislative “majority” elected by an obvious minority of the Statewide vote.

(3) It invites violent and disruptive protests if the normal liberal come-back, “plan to win the next election” looks forclosed by a rigged game.

Senate Republicans should invite House Democrats to negotiate an anti-gerrymandering civil rights bill both sides can live with.

States could be allowed leeway to experiment with methods to curb gerrymandering, eg non-partisan commissions, guidelines against ignoring county, town, and ward boundaries, etc. I suggest a State offer a popular vote between reapportionment plans offered by the largest and second-largest legislative coalitions. The weaker coalition would have every motive to offer an honest and sensible plan, since otherwise voters would ignore them.

but we all know that citizen-voting never significantly changes the government system status quo …due to a rigged system (e.g., Gerrymandering) controlled by the existing government.

Supreme Court is not some virtuous independent agency to control government excesses — it is an integral part of that government status quo … exercising far more arbitrary political power than citizen-voting.

SCOTUS Justices are merely ‘politicians’ drawn from the same political class as Congressmen. Trusting SCOTUS politicians is a major mistake.

Better to leave it to states to determine. This may see a move toward “non-partisan” redistricting commissions but I predict partisan bias will be (and likely has been) claimed for these allegedly non-partisan groups.