Its important to know that in anesthesia "private practice" doesnt always mean office based. Many hospitals contract an independant group practice to provide anesthesia, so even though thats technically a private practice you are still expected to provide night, holiday, and emergency coverage. You can however work in a surgicenter or in an endoscopy center and work an easy 9-5 job. Like anywhere else, the more you work the more you'll make. I am in a university program and attendings make $1000 per 12 hour (not even 24 hour) call. A group of only 7 or 8 of them take calls and on average they can take home an extra $5000 a month from those calls.
So in summary, yes you can get a job with no calls but you'll be able to afford a much nicer car if you do.