Would "For the People Act" (aka HR1) get required bipartisan support in the US Senate if it concentrated only on the prohibition of gerrymandering? Which political force is, at the present, the main profiteer of gerrymandering in the USA?
Impossible to say, but unlikely. Congressional Republicans have phrased the entire concept of federal regulation of voting as government overreach and a breach of the states's rights to do so. There's really no paring back of the bill which they could support without immediately undercutting that rhetoric.
Not to mention that their party as a whole has the most to gain from gerrymandering, as they control the substantial majority of redistricting processes in the nation, including in the "swing/battleground" states. The ideological war against the concept of gerrymandering simply hasn't advanced far enough for it to be worth it to Republicans to drop their greatest tool for achieving/retaining majority powers in state legislatures and the House. Which is not to say that Democrats in other states haven't gerrymandered when given the opportunity. Nor is it to say that Republicans universally will gerrymander wherever they can. But point of fact is that Republicans have far more opportunities (again), and they have been drowning their constituents in the rhetoric that further federal regulation of voting will destroy the chances of Republican majorities for decades to come, leaving themselves little room to negotiate and compromise.
Furthermore, the Senate minority is led by Mitch McConnell, the most aggressive and successful obstructionist in recent memory, and perhaps ever. He is, by his own public press conferences, 100% dedicated to stopping the objectives of this administration. To think there is any legitimate bipartisan action possible on something with any amount of partisan divide when one of the chamber's leaders has publicly taken a flamethrower to the very concept of it is, frankly, laughable.
Would "For the People Act" (aka HR1) get required bipartisan support in the US Senate if it concentrated only on the prohibition of gerrymandering?
No, because what one group of people call "gerrymandering" is what another group of people call "the right of their state legislature to determine how to send representatives to Congress."
The purpose of the US Senate is to represent the interests of states in Congress. Many states have decided, through their legislatures, that it is in their interests to draw their congressional districts in a blatantly partisan way that makes it easier for incumbents to get re-elected. State legislatures have the right under the Constitution to choose how to draw their congressional districts, regardless of whether the outcome of that process is sleazy or not.
Which political force is, at the present, the main profiteer of gerrymandering in the USA?
Evergreen answer: The same "political force" that explains most of the behavior of state legislatures: the desire of politicians who hold office today to get re-elected.
There is a current tendency to view the issue of gerrymandering as something the Republican Party does in order to degrade the Democratic Party's position in Congress from what it otherwise would be. While that may be the result of gerrymandering today, that isn't actually a very useful way to understand why gerrymandering happens and who benefits from it. The apparent partisan split in gerrymandering has only emerged recently because Republicans currently enjoy an advantage in controlling state governments that is historically atypical.
The simple fact is that politicians who are in office today are almost always primarily interested in getting re-elected tomorrow, and will do anything they can to make that easier. That's who benefits from gerrymandering.
There is a significant problem with not gerrymandering in the US system. It is a combination of two factors: (1) a de-facto two party system (2) single seat representation, with per-district winner-take-all, in legislatures at most levels of government.
To illustrate, let's say you have two parties, call them X and Y. Say you are looking at a state with 10 US Congressional districts (but the same principle applies to state legislatures etc). To start out, lets assume that voters for X and Y are uniformally distributed in the state, and that the statewide vote is 55% X and 45% Y. What happens? X wins every single seat. It is, prima facie, an unfair outcome.
Now in reality, the votes are not uniformally distributed. But neither are they split in a geographical way that makes various proposed "mathematically ideal" redistricting algorithm (e.g. minimize perimeter of district boundaries) produce an outcome both parties would find acceptable.
Instead, a process can be imposed (e.g. by the courts or federal government) where the two parties are forced to come up with a negotiation process for districting in which they gerrymander (i.e. manipulate the outcome) in such a way that both find it acceptable.
[addendum/update] Now it's very tempting to say "why don't we draw them in such a way that the voting populations, modulo the single-seat-winner-take-all rule, result in something resembling proportional representation"? That is what I would personally consider fair. Here's the problem with that - the history of the US and the way the electoral system is constructed explicitly rejects proportional representation. From what I can tell (secondhand, am not a lawyer or govt person), the legal/government world is clear on that point. So it would be a deep and fundamental change that both today's courts and legislatures may be unwilling to make, except to the limited extent necessary to correct blatant racial biases as should probably have been done long ago along the lines of the Civil Rights act.
Regardless of what you may have heard, HR 1 does not prevent gerrymandering. It merely changes who controls how the districts are drawn. But the new mechanism could be subverted, just as the old one has been.
There actually is a way to prevent it. One simply has to define a neutral, algorithmic way to set up the districts. For example, "least mean distance between two randomly-chosen voters in the same district." Requiring that the districts all have equal population of course. But no one seems to be interested in that.