I interviewed at Amazon in 2008ish and it was very leetcode-ish in its interview process. I remember whiteboarding a garbage collector.
In any event, few companies have product direction set by engineering. There might be influence, but product tends to be a different set of employees than engineering.
Every company I've worked for has had some form of annual or bi-annual "hack week," where employees can form ad-hoc teams and work on something they think would be cool to exist. Sometimes it's a feature, sometimes it's a new product line, sometimes it's just something ridiculous (e.g. an eight foot wide NES controller).
Some of these projects did turn into shipped features, though I'm not sure I ever saw a new product line come out of it.
One of the places I worked had an internal incubator. An engineer or PM could pitch an idea, and get paid their salary to go work on it if accepted. That was still early stage when I left, so unclear if anything came of it.
The point though is that many companies do open avenues for engineers to innovate directly.
I don't think you're necessarily disagreeing with the poster you're replying to.
I've interviewed at some of the FAANGs and like you said, I didn't find the Amazon interview format any less leetcode-ish than Google or Facebook. However I found that the level of rigor and was noticeably less than what Google or Facebook seemed to expect. Maybe this has changed recently, since the last time I interviewed at these companies was in 2019.
In any event, few companies have product direction set by engineering. There might be influence, but product tends to be a different set of employees than engineering.