After some back & forth I was able to (politely) prove their feedback was not correct, which actually granted me a follow-up interview.

Unfortunately, this was a unicorn, most companies don't give feedback, let alone admit they were wrong.

But, take-home is preferred, I want to use my IDE, with my keyboard shortcuts etc.

Then there are take-home timed challenges on systems like hackerrank / leetcode etc, which are horrible in terms of accessibility and access. Not to mention that they are a pass/fail, and focus purely on speed, not quality.

Next to that they don't allow you to work in an environment you're comfortable in. No debugger, etc. When an HVAC company hires a new tech, do they tell him/her to do a 1.5 hour repair with only a hammer and a lighter to diagnose and fix an issue? No, it's stupid. Why do developers have to do this then?

And the same applies to live coding exercises. While there is an opportunity to explain yourself, you're still in an extremely uncomfortable environment. Why is there such an emphasis to put people in an environment where they are not set up to succeed?