On the E3 visa - and AFAIK the H1B - you can't be out of work for more than 10 days. If you're not confident you can find a similar salary (and have an approved LCA) within that time then that makes the idea of rocking the boat a little more scary.
You can interview at, accept an offer from, apply for and receive a new LCA for another company all while continuing to work at your existing job. This means you have a new job and (preparatory documents for a new) visa set up before even giving notice and triggering the 10 day period. I know this from personal experience (on the E3).
More specifically: in a case where an H1B holder had concern for employer retaliation (say: working for a sketchy, illegal, or otherwise undesirable firm), and was looking for an option to leave (or possibly whistle blow), the fact that not having employment would be grounds for deportation within short order would be a constant threat.
I've known many people over the years who've had varying levels of frustrations with emigration issues. Many spent at least some of that time as undocumented, what some like to call "illegal", including working without authorization. For others it was merely the frustration of waiting while an impenetrable and slow process worked its way, with several having to make unavoidable trips out of country to be able to retain eligibility, often leaving work, friends, family, and homes for extended periods (sometimes with greater levels of support and assistance). And this isn't just a DESI situation: Europeans, Canadians, east Asians, doctors, programmers, healthcare professionals, researchers, nurses.
Most eventually settled in the US, some did not.
All had a considerable toll taken on them.