While it is true that ER docs don't drop out of the field itself, there is massive amount of job switching. I can't remember where I heard it, but something like 80% of ER docs switch jobs within 3 years of graduating residency. There is a high rate of burn-out with individual jobs and hospital locations. The grass is always greener, especially in Emergency Medicine. Many physicians find their comfortable niche where they stay for decades. Some are like migrant workers, following the local demand wherever that may lead every 3 years. For example, the current ER that I work has gone through over 20 ER docs in the past 5 years. Granted, some of those were locums, who never intended on staying.
My friend works at an ER where the hospital has fired 2 different ER groups over the past 3 years, resulting in massive turnover of dozens of physicians. My point is, I recommend you stay mobile if you choose EM as you really can't predict the political climate of a changeable administration. You may not know where you'll be in a few years when the new CEO/board/ER director/administration decide it is time for a change. They might want you gone and you might not tolerate the changes asked of you.