I've considered the congressional aspect you mentioned, but I don't think it solves the problem (at least in terms of a replacement), and I'll tell you why...
1) It's still going to be employed in a partisan fashion. No Democratic partisan congress is going to make a motion to pardon a well known Republican figure, and no Republican controlled congress is ever going to make a motion to pardon a well known Democratic figure.
Given that Democratic partisan presidents aren't much in the habit of pardoning well known Republican figures*, and vice versa, I don't see how this is particularly different. And before anyone says "well, what about Biden's preemptive pardons of Liz Cheney and Adam Kinzinger?" Well, (1) those pardons were not specific to them, but applied to the the entire January 6 Select Committee, and (2) both had effectively exited the Republican Party by that point (they endorsed Kamala Harris!), so I would say they no longer count as "well known Republican figures".
2) If it's a collaborative solution (where a president has to do it with the approval of congress), it's going to be viewed as obstructionist when the congress is not on the same team as the Pres, and viewed as a farcical formality ("rubber stamp") when congress is on the same side as the Pres.
I don't think it would be as much of a rubber stamp as people think it is. There's a reason why Presidents normally wait until the end of their terms to issue controversial pardons: Doing so is unpopular and one should try to do it at a time when it is unlikely to rebound either upon you or your party. But people in congress have much less luxury in regards to this. They have to worry about their next elections, particularly if they live in a swing state or swing district. Trump doesn't care if he takes heat for the current pardons he's doing or for the inevitable end-of-term-preemptive-pardons-of-every-member-of-his-family-and-staff that he's almost certainly going to issue just like Biden did. But if a congressman votes for those pardons, then they're going to have to explain to the voters next election "yeah, so here's why I did that." That demands greater accountability. Yes, I'm sure partisan politics will make congress much more subservient to what the President wants if the President is of their party, but there's still limits to that. As we've seen, even Trump has limits in getting the entire Republican congress to go along with something.
So all of the same challenges and perceptions of partisan bias will still be in full swing (just with extra steps)
it would, at least, appear to stop the particularly egregious pardons.
Now, I have heard an option that I've heard described that I've liked (though I don't know how practical it is) that still has a multi-branch collaboration element.
There's a pardon board (similar to a parole board) comprised of 7 members.
3 appointed by the Senate Majority leader
3 appointed by the Senate Minority leader
1 appointed by the Senate Parliamentarian
(and each of those positions has to be confirmed through the same process as cabinet appointments)
The president has the power to send pardon referrals to that panel, but it needs a 4-3 vote in favor to "pass".
This seems like it has multiple problems. The Senate Parliamentarian seems a position so far removed from anything like this that suddenly making them a kingmaker on something like this is problematic given it has nothing to do with their actual job;one might as well give the power to a bailiff of the Supreme Court. Further, the Senate Parliamentarian serves at the pleasure of the Senate Majority leader, who can just remove them at any time, meaning this functionally is a 4/3 in favor of the Senate majority.
Ultimately, this is a sticky wicket because of the fact that the founders (despite having many awesome ideas about checks and balances), didn't have a great solution or remediation element to the fact that the judicial branch has an outsized amount of power compared to the other 2.
And the judicial branch is the only one for which there's no rigid tangible standard by which to "un-do" what they do. (outside the branch itself)
But it isn't the "judicial branch" that actually convicts people. It's the jury, taken from the general public. I suppose someone could say a jury becomes part of the judicial branch, but it's on such a temporary basis I find that questionable. In any event, this might be an argument against removing any ability to ever pardon a guilty person, but again that's not the argument. The suggestion is to remove the pardoning power from the President and leave it to Congress, subject to the President's veto power. Congress, as far as I understand, already has that power (and if it doesn't, the same amendment process removing it from the President can give it to them).
And there are indeed ways to undo what the judicial branch does from outside. Some of them are roundabout (bringing in new judges to undo a decision, or in the case of convictions amending the law), but they're there.
In contrast, there is
nothing that can presently undo a pardon. Nothing. Once the President issues it, it's done. There is some question as to whether preemptive pardons are constitutional (they haven't been tested in court, in large part because I think prior to Biden only one preemptive pardon had ever been issued, namely Ford's pardon of Nixon, who subsequent Presidents didn't have interest in going after), but even if we restrict ourselves to pardons of crimes convicted, once it's done it's done.
No one can undo that pardon--not another branch, not even a different President. Even if a President gets impeached over corrupt pardons and kicked out of office, the pardons stick. Heck, if the impeachment process starts and it's certain the President will be kicked out, they can go on a pardoning spree before Congress can actually do their vote to kick them out. It strikes me as very odd in a system of checks and balance to give a power that
cannot be stopped or undone and is completely under the control of just one person who can do it at any time. So having pardons be passed like regular laws would actually be fixing the checks and balances system by having such an undoable power require two branches (Congress could do it by themselves if they have a veto proof majority).
Plus, the branch is unique in that the "Supremacy Clause" doesn't fully apply.
A state level judge technically has the power to say "I deem this federal law to be unconstitutional, so this state won't be enforcing it for the time being"
No such dynamic exists in the other two branches.
And then that judge can be overruled by a higher court. However, even if we grant this as a problem, how does the President have unilateral power to pardon solve it? The pardon power isn't about constitutional violations, but convictions. It's like saying "the justice system is too harsh on drug crimes so we should limit their power by increasing speed limits to make it harder to arrest people for speeding."
