Continuity of insurance is an issue. My wife currently requires a fairly expensive drug (thousand+ per dose), and gets 1-3 months supply at a time. With insurance, it's quite affordable. (separate rant)
Every time I switch employers, or my employers switch insurance, it begins a long process of getting the right info (the insurance always contracts out specialty drugs), then getting that info to the doctors office (Drs offices, btw, never make it easy to talk to someone), then the doctor has to send the info to the right insurance company (rare is the doctors office that follows through the first time), then the insurance company will sit on it for a while (I've heard crazy things like "it takes 48 hours before we can confirm that we got the fax, and only then can we begin to 'process' the fax, which can take 1 day to 1 week"), and probably reject it. Then I have to find out this happened (this is absurdly difficult), then the drs office can appeal. Last time the appeal actually involved my wife's doc talking to an insurance company doc on the phone! Thankfully, her doctor is unusually reachable and was willing to do this.
So, generally speaking, it takes 1-2 months before she can get the medication that prevents her from being effectively crippled. since the previous insurance gave 1-3 months at a time, she often ends up falling behind on doses when this occurs.
I've had 2 jobs in the last 5 years, but 5 insurance companies (my companies kept spinning off or getting absorbed), and each time the process was stressful, even though each health care plan was quite good, relative to most of the US. So I can see a healthcare argument as being highly relevant.
Add in those that work 1099 or other such arrangements, and it matters more.