Other than putting it all on Congress to fix, is your position that there is absolutely nothing that the Biden administration is responsible for?

Of course not. There are plenty of minor aspects of the border control system that Biden has some discretion in implementing. It's still his Department under his managerial authority, after all. If Congresspeople aren't being communicated with well, if they're not managing expectations or communications with communities that are being affected, if they're not allocating resources efficiently or effectively....all those things can have a modest impact at the margins of the issue. Whatever the fixed points of the immigration statutes and the budgetary resources, the Administration can play the hand they're dealt either badly or well.

But the fundamental core problem can't be addressed unilaterally, because (again) the core structure of our border control apparatus is just not set up for this problem. Our laws and the border patrol are geared mostly towards apprehending people who cross the border unlawfully or physically preventing them from getting more than a hundred yards into the country. Even that was always thought inadequate (people have been complaining about illegal immigration for decades), but it was a somewhat non-crisis level of inadequate - because most of the time, catching the people was enough. Because you just deported them.

Now that's changed. There's too many people who aren't trying to sneak into the country, and don't even try to get more than a hundred yards in before being apprehended. They're turning themselves in. And we don't have the laws or the resources to handle those people. All our resources are focused on catching them or keeping them stuck at the border. And that can't work under our current laws.

If you want the problem fixed in any meaningful way, Congress has to do it. If you want to leave the problem fundamentally unfixed, but criticize the Administration for not handling the unfixable problem better, there's always going to be room to find some areas of criticism. Even an unfixable problem can at least be responded to either well or poorly. But it's foolish to expect the Administration (any Administration) to actually fix the problem without Congressional action.