The advice to publish all the time feels overwhelming, but maybe it’s necessary to rise above the fray and get famous. Which is insane. That much quick turn around seems unhealthy. I think I’d need a break too.
Responsibility is on teachers to make time for writing, but it’s also up to education programs and professional development programs to provide teachers with ways to do it. The National Writing Project works on just these issues, which I recommend you check out if you haven’t.