"I know that every other candidate for the job successfully did this exercise but I found it too difficult to even set up. Can you hire me over all of them?"
What do you think the company's response will be?
If you accepted the take-home, and failed to get started on it, and then asked for something else, I wouldn't. Because I have evaluated other candidates and they were able to do it.
"Every other candidate was desperate and rejected a thousand times so they're happy to waste their time on your pointless exercise that you won't even look at."
The good candidates are busy getting hired by companies that understand how to evaluate their work based on interviews, references, and several other things that don't waste their time.
But there were also reports on HN that before the layoff wave, they'd get 2-3 applications per year for a senior position. It is of course any employers right to continue applying the same hiring standards as eg. FAANG/Big Tech would. But if I were the employer, a better strategy in such a situation would be to just swallow that I can't pick and choose if I have nothing to offer for leverage :)
I'm sure you're smart enough to realize that what I'm hinting at is that the job market is a _market_ and that employees don't have to put up with every bullshit depending on the market conditions.