That sounds wonderful, but it's gonna be hard to rule gerrymandering as unconstitutional. The parties involved would have to show proof that they're being packed into a district to benefit a party.
That's actually very easy to do. There are already computer algorithms that can gerrymander better than most groups of people. That means that the mathematical means exist to prove this definitively.
Even if you eliminate gerrymandering, I still don't think the Democrats will regain the House instantly.
In the 2012 election Democrats won 50.6% of the popular vote in the House but only occupied 46.2% of house seats. Now, part of that is the "small state/big state" effect, in which people who live in, say, Alaska or North Dakota get more congressional seats per capita than someone in New York or California. But gerrymandering is also a major part of that. The demographics of the country continue to become more diverse, giving the DNC the advantage. At that point, the GOP has to win on merit, not numbers.
The GOP has worked very hard to maintain barriers to voting. This is not a matter of principle for them, it is a matter of necessity. If we moved to an Australian system in which all citizens are required to submit a ballot (even if it's blank) and the government has a duty to facilitate this, it would be devastating for the current GOP. Overnight.
As its older white base dies, a younger more open minded base replaces it. I'm certain that if the GOP ever got to a socially neutral/fiscal conservative position it would be a force to be reckoned with. It's easy to accept that many Republicans couldn't care less about social issues: they're more fiscally minded. However, it's the whole guilt by association that has them down.
And if they can do that, then you are right. But the problem is that, as we have seen, you can't just kick people out of the GOP. That said, social conservative adults tend to raise social conservative kids. Here we are 70-odd years from the Civil Rights Act and we are still grappling with substantial structural, systemic, and sometimes overt racism. Back around the time of the CRA, the DNC and GOP very abruptly switched roles with respect to these issues (which must have been a thing to see) and that happened by tacit agreement between the two parties. Basically, the prejudiced people (and there are a lot of them) were willingly traded to the GOP by the DNC. But in this case, the DNC doesn't want those people back. The GOP can't kick them out (they can't; political parties work on democratic rules) and even if they could, there's nowhere for them to go. The only solution is to build a third party that is socially neutral or even socially liberal but fiscally conservative. The problem is that most liberals would still be voting en bloc for the DNC and so the RNC and the new party would split votes and the DNC would dominate until several election cycles into the future when the demographics had sorted out. If you've ever studied game theory, you can see why there are significant barriers to such a move.